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mizar/prime_scan.gp

Last active January 9, 2023 07:02
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整数環FFT用素数探索 (PARI/GP script)
Raw
prime_scan.gp
hex(n) =
{
return(if(n < 0, Strprintf("-0x%x", -n), Strprintf("0x%x", n)));
};
ban(n) =
{
local(b, c, v);
c = round(n);
v = "";
while(c != 0,
b = bitand(c, -c);
v = if(b > 2, Str(2 "^" length(binary(b - 1)) v), Str(b, v));
if(bitand(c, b + b) == 0,
c = c - b; v = Str(if(c != 0, " + ", ""), v),
c = c + b; v = Str(if(c != 0, " - ", "- "), v)
);
);
return(v);
};
fan(n, lim) =
{
local(f, v, k);
f = factor(round(n), lim);
v = "";
for(k = 1, length(f~), v = Str(v, if(k > 1, " * ", "") f[k, 1] if(f[k, 2] > 1, Str("^" f[k, 2]), if(isprime(f[k, 1]), "", "c"))));
return(v);
};
primescan(rv=[64], s=[2]) =
{
local(i, j, n, r, nv, nd, r2, sv, tv, uv, t, v, f);
for(j = 1, length(rv),
r = rv[j];
f = Strprintf("result_prime_%04d.yaml", r);
write(f, "- \"r\": " r);
write(f, " \"primes\":");
sv = vector(length(s), i, s[i]);
uv = vector(length(s), i, 1);
nv = vector(length(s), i, 2^r - ((2^r - 1) % s[i]));
for(i = 1, length(s), while(sv[i] > 0 && sv[i] % 2 == 0, sv[i] = sv[i] / 2; uv[i] = uv[i] * 2));
for(i = 1, length(s), while(nv[i] > 1 && !isprime(nv[i]), nv[i] = nv[i] - sv[i] * uv[i]));
while(1,
tv = vector(length(s), i, 1);
for(i = 1, length(s), while(nv[i] > 1 && nv[i] % 2^(tv[i]+1) == 1, tv[i] = tv[i] + 1));
v = 1; for(i = 1, length(s), if(nv[i] > 1 && (nv[v] < 2 || tv[v] > tv[i] || (tv[v] == tv[i] && nv[v] < nv[i])), v = i));
t = tv[v];
n = nv[v];
if(n < 2, break(),
for(i = 1, length(s), if(nv[i] == n, uv[i] = 2^tv[i]));
nd = lift(Mod(-1, 2^r) / n);
r2 = lift(Mod(4^r, n));
write(f, " - \"n\": " n);
write(f, " \"n_hex\": \"" hex(n) "\"");
write(f, " \"n_bit\": \"" ban(n) "\"");
write(f, " \"n_fac\": \"" fan(n - 1, 10000) " + 1\"");
write(f, " \"nd\": " nd);
write(f, " \"nd_hex\": \"" hex(nd) "\"");
write(f, " \"nd_bit\": \"" ban(nd) "\"");
write(f, " \"r2\": " r2);
write(f, " \"r2_hex\": \"" hex(r2) "\"");
write(f, " \"r2_bit\": \"" ban(r2) "\"");
if(n % 2^(max(r - 128, 1)) == 1,
write(f, " \"znprimroot\": " lift(znprimroot(n))));
for(i = 1, length(s), if(nv[i] == n,
nv[i] = nv[i] - sv[i] * uv[i];
uv[i] = uv[i] * 2;
while(nv[i] > 1 && !isprime(nv[i]), nv[i] = nv[i] - sv[i] * uv[i]);
));
);
);
);
};
allocatemem(2^25); \\ allocate memory 32MiB
primescan([14,15,16,22,23,24,25,26,30,31,32,46,47,48,49,50,51,52,58,59,60,61,62,63,64,94,95,96,100,101,102,103,104,126,127,128,190,191,192,254,255,256], [2, 2*3, 2*3*3, 2*3*5, 2*3*3*5, 2*3*5*7, 2*3*3*5*7]);
\\ primescan([384,512,768,1024], [2, 2*3, 2*3*3, 2*3*5, 2*3*3*5, 2*3*5*7, 2*3*3*5*7]); \\ heavy task
quit;
Raw
prime_scan.md

整数環FFT用素数探索 (PARI/GP Script)

出力要素

  • n: 素数
  • nd: -1 / n (mod 2^r)
  • r2: (2^r)^2 (mod n)
  • znprimroot: 原始根
  • _hex: 16進数表記
  • _bit: 2進bit加減算表記
  • _fac: (n-1)の素因数分解(抄)表記, 末尾'c'の因数は合成数を示す

実行コマンド例

rm result_prime_*.yaml; gp prime_scan.gp

参考

Raw
result_prime_0014.yaml
- "r": 14
"primes":
- "n": 16381
"n_hex": "0x3ffd"
"n_bit": "2^14 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5 * 7 * 13 + 1"
"nd": 10923
"nd_hex": "0x2aab"
"nd_bit": "2^14 - 2^12 - 2^10 - 2^8 - 2^6 - 2^4 - 2^2 - 1"
"r2": 9
"r2_hex": "0x9"
"r2_bit": "2^3 + 1"
"znprimroot": 2
- "n": 16369
"n_hex": "0x3ff1"
"n_bit": "2^14 - 2^4 + 1"
"n_fac": "2^4 * 3 * 11 * 31 + 1"
"nd": 12015
"nd_hex": "0x2eef"
"nd_bit": "2^14 - 2^12 - 2^8 - 2^4 - 1"
"r2": 225
"r2_hex": "0xe1"
"r2_bit": "2^8 - 2^5 + 1"
"znprimroot": 7
- "n": 16273
"n_hex": "0x3f91"
"n_bit": "2^14 - 2^7 + 2^4 + 1"
"n_fac": "2^4 * 3^2 * 113 + 1"
"nd": 7823
"nd_hex": "0x1e8f"
"nd_bit": "2^13 - 2^9 + 2^7 + 2^4 - 1"
"r2": 12321
"r2_hex": "0x3021"
"r2_bit": "2^14 - 2^12 + 2^5 + 1"
"znprimroot": 7
- "n": 15601
"n_hex": "0x3cf1"
"n_bit": "2^14 - 2^10 + 2^8 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5^2 * 13 + 1"
"nd": 3055
"nd_hex": "0xbef"
"nd_bit": "2^12 - 2^10 - 2^4 - 1"
"r2": 4650
"r2_hex": "0x122a"
"r2_bit": "2^12 + 2^9 + 2^5 + 2^3 + 2"
"znprimroot": 23
- "n": 15121
"n_hex": "0x3b11"
"n_bit": "2^14 - 2^10 - 2^8 + 2^4 + 1"
"n_fac": "2^4 * 3^3 * 5 * 7 + 1"
"nd": 10767
"nd_hex": "0x2a0f"
"nd_bit": "2^13 + 2^11 + 2^9 + 2^4 - 1"
"r2": 7464
"r2_hex": "0x1d28"
"r2_bit": "2^13 - 2^10 + 2^8 + 2^5 + 2^3"
"znprimroot": 11
- "n": 16033
"n_hex": "0x3ea1"
"n_bit": "2^14 - 2^9 + 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3 * 167 + 1"
"nd": 6815
"nd_hex": "0x1a9f"
"nd_bit": "2^13 - 2^11 + 2^9 + 2^7 + 2^5 - 1"
"r2": 10970
"r2_hex": "0x2ada"
"r2_bit": "2^14 - 2^12 - 2^10 - 2^8 - 2^5 - 2^3 + 2"
"znprimroot": 5
- "n": 16193
"n_hex": "0x3f41"
"n_bit": "2^14 - 2^8 + 2^6 + 1"
"n_fac": "2^6 * 11 * 23 + 1"
"nd": 12095
"nd_hex": "0x2f3f"
"nd_bit": "2^14 - 2^12 - 2^8 + 2^6 - 1"
"r2": 4095
"r2_hex": "0xfff"
"r2_bit": "2^12 - 1"
"znprimroot": 5
- "n": 15937
"n_hex": "0x3e41"
"n_bit": "2^14 - 2^9 + 2^6 + 1"
"n_fac": "2^6 * 3 * 83 + 1"
"nd": 11839
"nd_hex": "0x2e3f"
"nd_bit": "2^14 - 2^12 - 2^9 + 2^6 - 1"
"r2": 8565
"r2_hex": "0x2175"
"r2_bit": "2^13 + 2^9 - 2^7 - 2^4 + 2^2 + 1"
"znprimroot": 7
- "n": 14401
"n_hex": "0x3841"
"n_bit": "2^14 - 2^11 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5^2 + 1"
"nd": 10303
"nd_hex": "0x283f"
"nd_bit": "2^13 + 2^11 + 2^6 - 1"
"r2": 816
"r2_hex": "0x330"
"r2_bit": "2^10 - 2^8 + 2^6 - 2^4"
"znprimroot": 11
- "n": 16001
"n_hex": "0x3e81"
"n_bit": "2^14 - 2^9 + 2^7 + 1"
"n_fac": "2^7 * 5^3 + 1"
"nd": 15999
"nd_hex": "0x3e7f"
"nd_bit": "2^14 - 2^9 + 2^7 - 1"
"r2": 2680
"r2_hex": "0xa78"
"r2_bit": "2^11 + 2^9 + 2^7 - 2^3"
"znprimroot": 3
- "n": 13441
"n_hex": "0x3481"
"n_bit": "2^14 - 2^12 + 2^10 + 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 7 + 1"
"nd": 13439
"nd_hex": "0x347f"
"nd_bit": "2^14 - 2^12 + 2^10 + 2^7 - 1"
"r2": 5245
"r2_hex": "0x147d"
"r2_bit": "2^12 + 2^10 + 2^7 - 2^2 + 1"
"znprimroot": 11
- "n": 10369
"n_hex": "0x2881"
"n_bit": "2^13 + 2^11 + 2^7 + 1"
"n_fac": "2^7 * 3^4 + 1"
"nd": 10367
"nd_hex": "0x287f"
"nd_bit": "2^13 + 2^11 + 2^7 - 1"
"r2": 2784
"r2_hex": "0xae0"
"r2_bit": "2^12 - 2^10 - 2^8 - 2^5"
"znprimroot": 13
- "n": 15361
"n_hex": "0x3c01"
"n_bit": "2^14 - 2^10 + 1"
"n_fac": "2^10 * 3 * 5 + 1"
"nd": 15359
"nd_hex": "0x3bff"
"nd_bit": "2^14 - 2^10 - 1"
"r2": 1981
"r2_hex": "0x7bd"
"r2_bit": "2^11 - 2^6 - 2^2 + 1"
"znprimroot": 7
- "n": 12289
"n_hex": "0x3001"
"n_bit": "2^14 - 2^12 + 1"
"n_fac": "2^12 * 3 + 1"
"nd": 12287
"nd_hex": "0x2fff"
"nd_bit": "2^14 - 2^12 - 1"
"r2": 6829
"r2_hex": "0x1aad"
"r2_bit": "2^13 - 2^10 - 2^8 - 2^6 - 2^4 - 2^2 + 1"
"znprimroot": 11
Raw
result_prime_0015.yaml
- "r": 15
"primes":
- "n": 32707
"n_hex": "0x7fc3"
"n_bit": "2^15 - 2^6 + 2^2 - 1"
"n_fac": "2 * 3^2 * 23 * 79 + 1"
"nd": 5909
"nd_hex": "0x1715"
"nd_bit": "2^13 - 2^11 - 2^8 + 2^4 + 2^2 + 1"
"r2": 3721
"r2_hex": "0xe89"
"r2_bit": "2^12 - 2^9 + 2^7 + 2^3 + 1"
"znprimroot": 3
- "n": 32611
"n_hex": "0x7f63"
"n_bit": "2^15 - 2^7 - 2^5 + 2^2 - 1"
"n_fac": "2 * 3 * 5 * 1087 + 1"
"nd": 1461
"nd_hex": "0x5b5"
"nd_bit": "2^11 - 2^9 - 2^6 - 2^4 + 2^2 + 1"
"r2": 24649
"r2_hex": "0x6049"
"r2_bit": "2^15 - 2^13 + 2^6 + 2^3 + 1"
"znprimroot": 3
- "n": 32491
"n_hex": "0x7eeb"
"n_bit": "2^15 - 2^8 - 2^4 - 2^2 - 1"
"n_fac": "2 * 3^2 * 5 * 19^2 + 1"
"nd": 17981
"nd_hex": "0x463d"
"nd_bit": "2^14 + 2^11 - 2^9 + 2^6 - 2^2 + 1"
"r2": 11747
"r2_hex": "0x2de3"
"r2_bit": "2^14 - 2^12 - 2^9 - 2^5 + 2^2 - 1"
"znprimroot": 2
- "n": 30871
"n_hex": "0x7897"
"n_bit": "2^15 - 2^11 + 2^7 + 2^5 - 2^3 - 1"
"n_fac": "2 * 3^2 * 5 * 7^3 + 1"
"nd": 30937
"nd_hex": "0x78d9"
"nd_bit": "2^15 - 2^11 + 2^8 - 2^5 - 2^3 + 1"
"r2": 17573
"r2_hex": "0x44a5"
"r2_bit": "2^14 + 2^10 + 2^7 + 2^5 + 2^2 + 1"
"znprimroot": 3
- "n": 32749
"n_hex": "0x7fed"
"n_bit": "2^15 - 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3 * 2729 + 1"
"nd": 18971
"nd_hex": "0x4a1b"
"nd_bit": "2^14 + 2^11 + 2^9 + 2^5 - 2^2 - 1"
"r2": 361
"r2_hex": "0x169"
"r2_bit": "2^9 - 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 2
- "n": 32653
"n_hex": "0x7f8d"
"n_bit": "2^15 - 2^7 + 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 907 + 1"
"nd": 9403
"nd_hex": "0x24bb"
"nd_bit": "2^13 + 2^10 + 2^8 - 2^6 - 2^2 - 1"
"r2": 13225
"r2_hex": "0x33a9"
"r2_bit": "2^14 - 2^12 + 2^10 - 2^7 + 2^5 + 2^3 + 1"
"znprimroot": 2
- "n": 32341
"n_hex": "0x7e55"
"n_bit": "2^15 - 2^9 + 2^6 + 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 7^2 * 11 + 1"
"nd": 28931
"nd_hex": "0x7103"
"nd_bit": "2^15 - 2^12 + 2^8 + 2^2 - 1"
"r2": 20624
"r2_hex": "0x5090"
"r2_bit": "2^14 + 2^12 + 2^7 + 2^4"
"znprimroot": 2
- "n": 32713
"n_hex": "0x7fc9"
"n_bit": "2^15 - 2^6 + 2^3 + 1"
"n_fac": "2^3 * 3 * 29 * 47 + 1"
"nd": 13703
"nd_hex": "0x3587"
"nd_bit": "2^14 - 2^11 - 2^9 - 2^7 + 2^3 - 1"
"r2": 3025
"r2_hex": "0xbd1"
"r2_bit": "2^12 - 2^10 - 2^6 + 2^4 + 1"
"znprimroot": 5
- "n": 31081
"n_hex": "0x7969"
"n_bit": "2^15 - 2^11 + 2^9 - 2^7 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 7 * 37 + 1"
"nd": 22823
"nd_hex": "0x5927"
"nd_bit": "2^15 - 2^13 - 2^11 + 2^8 + 2^5 + 2^3 - 1"
"r2": 17598
"r2_hex": "0x44be"
"r2_bit": "2^14 + 2^10 + 2^8 - 2^6 - 2"
"znprimroot": 13
- "n": 32497
"n_hex": "0x7ef1"
"n_bit": "2^15 - 2^8 - 2^4 + 1"
"n_fac": "2^4 * 3 * 677 + 1"
"nd": 19951
"nd_hex": "0x4def"
"nd_bit": "2^14 + 2^12 - 2^9 - 2^4 - 1"
"r2": 8447
"r2_hex": "0x20ff"
"r2_bit": "2^13 + 2^8 - 1"
"znprimroot": 7
- "n": 32401
"n_hex": "0x7e91"
"n_bit": "2^15 - 2^9 + 2^7 + 2^4 + 1"
"n_fac": "2^4 * 3^4 * 5^2 + 1"
"nd": 32143
"nd_hex": "0x7d8f"
"nd_bit": "2^15 - 2^9 - 2^7 + 2^4 - 1"
"r2": 5085
"r2_hex": "0x13dd"
"r2_bit": "2^12 + 2^10 - 2^5 - 2^2 + 1"
"znprimroot": 7
- "n": 32609
"n_hex": "0x7f61"
"n_bit": "2^15 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 1019 + 1"
"nd": 7007
"nd_hex": "0x1b5f"
"nd_bit": "2^13 - 2^10 - 2^7 - 2^5 - 1"
"r2": 25281
"r2_hex": "0x62c1"
"r2_bit": "2^15 - 2^13 + 2^10 - 2^8 - 2^6 + 1"
"znprimroot": 3
- "n": 32353
"n_hex": "0x7e61"
"n_bit": "2^15 - 2^9 + 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3 * 337 + 1"
"nd": 23135
"nd_hex": "0x5a5f"
"nd_bit": "2^15 - 2^13 - 2^11 + 2^9 + 2^7 - 2^5 - 1"
"r2": 10460
"r2_hex": "0x28dc"
"r2_bit": "2^13 + 2^11 + 2^8 - 2^5 - 2^2"
"znprimroot": 15
- "n": 30241
"n_hex": "0x7621"
"n_bit": "2^15 - 2^11 - 2^9 + 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5 * 7 + 1"
"nd": 29215
"nd_hex": "0x721f"
"nd_bit": "2^15 - 2^12 + 2^9 + 2^5 - 1"
"r2": 4878
"r2_hex": "0x130e"
"r2_bit": "2^12 + 2^10 - 2^8 + 2^4 - 2"
"znprimroot": 11
- "n": 32321
"n_hex": "0x7e41"
"n_bit": "2^15 - 2^9 + 2^6 + 1"
"n_fac": "2^6 * 5 * 101 + 1"
"nd": 28223
"nd_hex": "0x6e3f"
"nd_bit": "2^15 - 2^12 - 2^9 + 2^6 - 1"
"r2": 5883
"r2_hex": "0x16fb"
"r2_bit": "2^13 - 2^11 - 2^8 - 2^2 - 1"
"znprimroot": 6
- "n": 29761
"n_hex": "0x7441"
"n_bit": "2^15 - 2^12 + 2^10 + 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 31 + 1"
"nd": 25663
"nd_hex": "0x643f"
"nd_bit": "2^15 - 2^13 + 2^10 + 2^6 - 1"
"r2": 24466
"r2_hex": "0x5f92"
"r2_bit": "2^15 - 2^13 - 2^7 + 2^4 + 2"
"znprimroot": 17
- "n": 20161
"n_hex": "0x4ec1"
"n_bit": "2^14 + 2^12 - 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 7 + 1"
"nd": 16063
"nd_hex": "0x3ebf"
"nd_bit": "2^14 - 2^8 - 2^6 - 1"
"r2": 7286
"r2_hex": "0x1c76"
"r2_bit": "2^13 - 2^10 + 2^7 - 2^3 - 2"
"znprimroot": 13
- "n": 26881
"n_hex": "0x6901"
"n_bit": "2^15 - 2^13 + 2^11 + 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 7 + 1"
"nd": 26879
"nd_hex": "0x68ff"
"nd_bit": "2^15 - 2^13 + 2^11 + 2^8 - 1"
"r2": 7160
"r2_hex": "0x1bf8"
"r2_bit": "2^13 - 2^10 - 2^3"
"znprimroot": 11
- "n": 32257
"n_hex": "0x7e01"
"n_bit": "2^15 - 2^9 + 1"
"n_fac": "2^9 * 3^2 * 7 + 1"
"nd": 32255
"nd_hex": "0x7dff"
"nd_bit": "2^15 - 2^9 - 1"
"r2": 3065
"r2_hex": "0xbf9"
"r2_bit": "2^12 - 2^10 - 2^3 + 1"
"znprimroot": 15
- "n": 23041
"n_hex": "0x5a01"
"n_bit": "2^15 - 2^13 - 2^11 + 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5 + 1"
"nd": 23039
"nd_hex": "0x59ff"
"nd_bit": "2^15 - 2^13 - 2^11 + 2^9 - 1"
"r2": 8183
"r2_hex": "0x1ff7"
"r2_bit": "2^13 - 2^3 - 1"
"znprimroot": 11
- "n": 25601
"n_hex": "0x6401"
"n_bit": "2^15 - 2^13 + 2^10 + 1"
"n_fac": "2^10 * 5^2 + 1"
"nd": 25599
"nd_hex": "0x63ff"
"nd_bit": "2^15 - 2^13 + 2^10 - 1"
"r2": 10283
"r2_hex": "0x282b"
"r2_bit": "2^13 + 2^11 + 2^6 - 2^4 - 2^2 - 1"
"znprimroot": 3
- "n": 15361
"n_hex": "0x3c01"
"n_bit": "2^14 - 2^10 + 1"
"n_fac": "2^10 * 3 * 5 + 1"
"nd": 15359
"nd_hex": "0x3bff"
"nd_bit": "2^14 - 2^10 - 1"
"r2": 7924
"r2_hex": "0x1ef4"
"r2_bit": "2^13 - 2^8 - 2^4 + 2^2"
"znprimroot": 7
- "n": 18433
"n_hex": "0x4801"
"n_bit": "2^14 + 2^11 + 1"
"n_fac": "2^11 * 3^2 + 1"
"nd": 18431
"nd_hex": "0x47ff"
"nd_bit": "2^14 + 2^11 - 1"
"r2": 1141
"r2_hex": "0x475"
"r2_bit": "2^10 + 2^7 - 2^4 + 2^2 + 1"
"znprimroot": 5
- "n": 12289
"n_hex": "0x3001"
"n_bit": "2^14 - 2^12 + 1"
"n_fac": "2^12 * 3 + 1"
"nd": 12287
"nd_hex": "0x2fff"
"nd_bit": "2^14 - 2^12 - 1"
"r2": 2738
"r2_hex": "0xab2"
"r2_bit": "2^12 - 2^10 - 2^8 - 2^6 - 2^4 + 2"
"znprimroot": 11
Raw
result_prime_0016.yaml
- "r": 16
"primes":
- "n": 65521
"n_hex": "0xfff1"
"n_bit": "2^16 - 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5 * 7 * 13 + 1"
"nd": 61167
"nd_hex": "0xeeef"
"nd_bit": "2^16 - 2^12 - 2^8 - 2^4 - 1"
"r2": 225
"r2_hex": "0xe1"
"r2_bit": "2^8 - 2^5 + 1"
"znprimroot": 17
- "n": 63841
"n_hex": "0xf961"
"n_bit": "2^16 - 2^11 + 2^9 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 7 * 19 + 1"
"nd": 38239
"nd_hex": "0x955f"
"nd_bit": "2^15 + 2^13 - 2^11 - 2^9 - 2^7 - 2^5 - 1"
"r2": 180
"r2_hex": "0xb4"
"r2_bit": "2^8 - 2^6 - 2^4 + 2^2"
"znprimroot": 17
- "n": 30241
"n_hex": "0x7621"
"n_bit": "2^15 - 2^11 - 2^9 + 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5 * 7 + 1"
"nd": 29215
"nd_hex": "0x721f"
"nd_bit": "2^15 - 2^12 + 2^9 + 2^5 - 1"
"r2": 19512
"r2_hex": "0x4c38"
"r2_bit": "2^14 + 2^12 - 2^10 + 2^6 - 2^3"
"znprimroot": 11
- "n": 65089
"n_hex": "0xfe41"
"n_bit": "2^16 - 2^9 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 113 + 1"
"nd": 60991
"nd_hex": "0xee3f"
"nd_bit": "2^16 - 2^12 - 2^9 + 2^6 - 1"
"r2": 4542
"r2_hex": "0x11be"
"r2_bit": "2^12 + 2^9 - 2^6 - 2"
"znprimroot": 7
- "n": 47041
"n_hex": "0xb7c1"
"n_bit": "2^16 - 2^14 - 2^11 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 7^2 + 1"
"nd": 42943
"nd_hex": "0xa7bf"
"nd_bit": "2^15 + 2^13 + 2^11 - 2^6 - 1"
"r2": 29914
"r2_hex": "0x74da"
"r2_bit": "2^15 - 2^12 + 2^10 + 2^8 - 2^5 - 2^3 + 2"
"znprimroot": 29
- "n": 20161
"n_hex": "0x4ec1"
"n_bit": "2^14 + 2^12 - 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 7 + 1"
"nd": 48831
"nd_hex": "0xbebf"
"nd_bit": "2^16 - 2^14 - 2^8 - 2^6 - 1"
"r2": 8983
"r2_hex": "0x2317"
"r2_bit": "2^13 + 2^10 - 2^8 + 2^5 - 2^3 - 1"
"znprimroot": 13
- "n": 63361
"n_hex": "0xf781"
"n_bit": "2^16 - 2^11 - 2^7 + 1"
"n_fac": "2^7 * 3^2 * 5 * 11 + 1"
"nd": 46975
"nd_hex": "0xb77f"
"nd_bit": "2^16 - 2^14 - 2^11 - 2^7 - 1"
"r2": 41911
"r2_hex": "0xa3b7"
"r2_bit": "2^15 + 2^13 + 2^10 - 2^6 - 2^3 - 1"
"znprimroot": 37
- "n": 57601
"n_hex": "0xe101"
"n_bit": "2^16 - 2^13 + 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5^2 + 1"
"nd": 57599
"nd_hex": "0xe0ff"
"nd_bit": "2^16 - 2^13 + 2^8 - 1"
"r2": 6332
"r2_hex": "0x18bc"
"r2_bit": "2^13 - 2^11 + 2^8 - 2^6 - 2^2"
"znprimroot": 7
- "n": 26881
"n_hex": "0x6901"
"n_bit": "2^15 - 2^13 + 2^11 + 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 7 + 1"
"nd": 26879
"nd_hex": "0x68ff"
"nd_bit": "2^15 - 2^13 + 2^11 + 2^8 - 1"
"r2": 1759
"r2_hex": "0x6df"
"r2_bit": "2^11 - 2^8 - 2^5 - 1"
"znprimroot": 11
- "n": 23041
"n_hex": "0x5a01"
"n_bit": "2^15 - 2^13 - 2^11 + 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5 + 1"
"nd": 23039
"nd_hex": "0x59ff"
"nd_bit": "2^15 - 2^13 - 2^11 + 2^9 - 1"
"r2": 9691
"r2_hex": "0x25db"
"r2_bit": "2^13 + 2^11 - 2^9 - 2^5 - 2^2 - 1"
"znprimroot": 11
- "n": 64513
"n_hex": "0xfc01"
"n_bit": "2^16 - 2^10 + 1"
"n_fac": "2^10 * 3^2 * 7 + 1"
"nd": 64511
"nd_hex": "0xfbff"
"nd_bit": "2^16 - 2^10 - 1"
"r2": 14321
"r2_hex": "0x37f1"
"r2_bit": "2^14 - 2^11 - 2^4 + 1"
"znprimroot": 5
- "n": 18433
"n_hex": "0x4801"
"n_bit": "2^14 + 2^11 + 1"
"n_fac": "2^11 * 3^2 + 1"
"nd": 18431
"nd_hex": "0x47ff"
"nd_bit": "2^14 + 2^11 - 1"
"r2": 4564
"r2_hex": "0x11d4"
"r2_bit": "2^12 + 2^9 - 2^6 + 2^4 + 2^2"
"znprimroot": 5
- "n": 61441
"n_hex": "0xf001"
"n_bit": "2^16 - 2^12 + 1"
"n_fac": "2^12 * 3 * 5 + 1"
"nd": 61439
"nd_hex": "0xefff"
"nd_bit": "2^16 - 2^12 - 1"
"r2": 57073
"r2_hex": "0xdef1"
"r2_bit": "2^16 - 2^13 - 2^8 - 2^4 + 1"
"znprimroot": 17
- "n": 40961
"n_hex": "0xa001"
"n_bit": "2^15 + 2^13 + 1"
"n_fac": "2^13 * 5 + 1"
"nd": 40959
"nd_hex": "0x9fff"
"nd_bit": "2^15 + 2^13 - 1"
"r2": 1641
"r2_hex": "0x669"
"r2_bit": "2^11 - 2^9 + 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 3
Raw
result_prime_0022.yaml
- "r": 22
"primes":
- "n": 4194271
"n_hex": "0x3fffdf"
"n_bit": "2^22 - 2^5 - 1"
"n_fac": "2 * 3^2 * 5 * 29 * 1607 + 1"
"nd": 1016801
"nd_hex": "0xf83e1"
"nd_bit": "2^20 - 2^15 + 2^10 - 2^5 + 1"
"r2": 1089
"r2_hex": "0x441"
"r2_bit": "2^10 + 2^6 + 1"
"znprimroot": 6
- "n": 4194301
"n_hex": "0x3ffffd"
"n_bit": "2^22 - 2^2 + 1"
"n_fac": "2^2 * 3 * 5^2 * 11 * 31 * 41 + 1"
"nd": 2796203
"nd_hex": "0x2aaaab"
"nd_bit": "2^22 - 2^20 - 2^18 - 2^16 - 2^14 - 2^12 - 2^10 - 2^8 - 2^6 - 2^4 - 2^2 - 1"
"r2": 9
"r2_hex": "0x9"
"r2_bit": "2^3 + 1"
"znprimroot": 7
- "n": 4194181
"n_hex": "0x3fff85"
"n_bit": "2^22 - 2^7 + 2^2 + 1"
"n_fac": "2^2 * 3^5 * 5 * 863 + 1"
"nd": 3137203
"nd_hex": "0x2fdeb3"
"nd_bit": "2^22 - 2^20 - 2^13 - 2^8 - 2^6 - 2^4 + 2^2 - 1"
"r2": 15129
"r2_hex": "0x3b19"
"r2_bit": "2^14 - 2^10 - 2^8 + 2^5 - 2^3 + 1"
"znprimroot": 7
- "n": 4193701
"n_hex": "0x3ffda5"
"n_bit": "2^22 - 2^9 - 2^7 + 2^5 + 2^2 + 1"
"n_fac": "2^2 * 3 * 5^2 * 7 * 1997 + 1"
"nd": 1662419
"nd_hex": "0x195dd3"
"nd_bit": "2^21 - 2^19 + 2^17 - 2^15 - 2^13 - 2^9 - 2^6 + 2^4 + 2^2 - 1"
"r2": 363609
"r2_hex": "0x58c59"
"r2_bit": "2^19 - 2^17 - 2^15 + 2^12 - 2^10 + 2^7 - 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 4192021
"n_hex": "0x3ff715"
"n_bit": "2^22 - 2^11 - 2^8 + 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3^3 * 5 * 7 * 1109 + 1"
"nd": 4087747
"nd_hex": "0x3e5fc3"
"nd_bit": "2^22 - 2^17 + 2^15 - 2^13 - 2^6 + 2^2 - 1"
"r2": 1020068
"r2_hex": "0xf90a4"
"r2_bit": "2^20 - 2^15 + 2^12 + 2^7 + 2^5 + 2^2"
"znprimroot": 10
- "n": 4194217
"n_hex": "0x3fffa9"
"n_bit": "2^22 - 2^7 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 13 * 4481 + 1"
"nd": 1108839
"nd_hex": "0x10eb67"
"nd_bit": "2^20 + 2^16 - 2^12 - 2^10 - 2^7 - 2^5 + 2^3 - 1"
"r2": 7569
"r2_hex": "0x1d91"
"r2_bit": "2^13 - 2^9 - 2^7 + 2^4 + 1"
"znprimroot": 5
- "n": 4170601
"n_hex": "0x3fa369"
"n_bit": "2^22 - 2^15 + 2^13 + 2^10 - 2^7 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5^2 * 7 * 331 + 1"
"nd": 2679591
"nd_hex": "0x28e327"
"nd_bit": "2^21 + 2^19 + 2^16 - 2^13 + 2^10 - 2^8 + 2^5 + 2^3 - 1"
"r2": 2971675
"r2_hex": "0x2d581b"
"r2_bit": "2^22 - 2^20 - 2^17 - 2^15 - 2^13 - 2^11 + 2^5 - 2^2 - 1"
"znprimroot": 13
- "n": 4193041
"n_hex": "0x3ffb11"
"n_bit": "2^22 - 2^10 - 2^8 + 2^4 + 1"
"n_fac": "2^4 * 3 * 5 * 17471 + 1"
"nd": 1550863
"nd_hex": "0x17aa0f"
"nd_bit": "2^21 - 2^19 - 2^15 + 2^13 + 2^11 + 2^9 + 2^4 - 1"
"r2": 1595169
"r2_hex": "0x185721"
"r2_bit": "2^21 - 2^19 + 2^15 - 2^13 - 2^11 - 2^8 + 2^5 + 1"
"znprimroot": 13
- "n": 4192561
"n_hex": "0x3ff931"
"n_bit": "2^22 - 2^11 + 2^8 + 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3^4 * 5 * 647 + 1"
"nd": 344111
"nd_hex": "0x5402f"
"nd_bit": "2^18 + 2^16 + 2^14 + 2^6 - 2^4 - 1"
"r2": 3038049
"r2_hex": "0x2e5b61"
"r2_bit": "2^22 - 2^20 - 2^17 + 2^15 - 2^13 - 2^10 - 2^7 - 2^5 + 1"
"znprimroot": 19
- "n": 4184881
"n_hex": "0x3fdb31"
"n_bit": "2^22 - 2^13 - 2^10 - 2^8 + 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5 * 7 * 47 * 53 + 1"
"nd": 4088367
"nd_hex": "0x3e622f"
"nd_bit": "2^22 - 2^17 + 2^15 - 2^13 + 2^9 + 2^6 - 2^4 - 1"
"r2": 910428
"r2_hex": "0xde45c"
"r2_bit": "2^20 - 2^17 - 2^13 + 2^10 + 2^7 - 2^5 - 2^2"
"znprimroot": 11
- "n": 4193633
"n_hex": "0x3ffd61"
"n_bit": "2^22 - 2^9 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 29 * 4519 + 1"
"nd": 1218911
"nd_hex": "0x12995f"
"nd_bit": "2^20 + 2^17 + 2^15 + 2^13 - 2^11 + 2^9 - 2^7 - 2^5 - 1"
"r2": 450241
"r2_hex": "0x6dec1"
"r2_bit": "2^19 - 2^16 - 2^13 - 2^8 - 2^6 + 1"
"znprimroot": 3
- "n": 4193569
"n_hex": "0x3ffd21"
"n_bit": "2^22 - 2^10 + 2^8 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 14561 + 1"
"nd": 2373919
"nd_hex": "0x24391f"
"nd_bit": "2^21 + 2^18 + 2^14 - 2^11 + 2^8 + 2^5 - 1"
"r2": 540225
"r2_hex": "0x83e41"
"r2_bit": "2^19 + 2^14 - 2^9 + 2^6 + 1"
"znprimroot": 11
- "n": 4185121
"n_hex": "0x3fdc21"
"n_bit": "2^22 - 2^13 - 2^10 + 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 8719 + 1"
"nd": 3758111
"nd_hex": "0x39581f"
"nd_bit": "2^22 - 2^19 + 2^17 - 2^15 - 2^13 - 2^11 + 2^5 - 1"
"r2": 625069
"r2_hex": "0x989ad"
"r2_bit": "2^19 + 2^17 - 2^15 + 2^11 + 2^9 - 2^6 - 2^4 - 2^2 + 1"
"znprimroot": 11
- "n": 4163041
"n_hex": "0x3f85e1"
"n_bit": "2^22 - 2^15 + 2^11 - 2^9 - 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 7^2 * 59 + 1"
"nd": 3441119
"nd_hex": "0x3481df"
"nd_bit": "2^22 - 2^20 + 2^18 + 2^15 + 2^9 - 2^5 - 1"
"r2": 3223575
"r2_hex": "0x313017"
"r2_bit": "2^22 - 2^20 + 2^16 + 2^14 - 2^12 + 2^5 - 2^3 - 1"
"znprimroot": 19
- "n": 4193089
"n_hex": "0x3ffb41"
"n_bit": "2^22 - 2^10 - 2^8 + 2^6 + 1"
"n_fac": "2^6 * 3 * 21839 + 1"
"nd": 4025151
"nd_hex": "0x3d6b3f"
"nd_bit": "2^22 - 2^17 - 2^15 - 2^12 - 2^10 - 2^8 + 2^6 - 1"
"r2": 1476225
"r2_hex": "0x168681"
"r2_bit": "2^21 - 2^19 - 2^17 + 2^15 + 2^11 - 2^9 + 2^7 + 1"
"znprimroot": 11
- "n": 4184641
"n_hex": "0x3fda41"
"n_bit": "2^22 - 2^13 - 2^11 + 2^9 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 1453 + 1"
"nd": 1231423
"nd_hex": "0x12ca3f"
"nd_bit": "2^20 + 2^18 - 2^16 - 2^14 + 2^11 + 2^9 + 2^6 - 1"
"r2": 1311467
"r2_hex": "0x1402eb"
"r2_bit": "2^20 + 2^18 + 2^10 - 2^8 - 2^4 - 2^2 - 1"
"znprimroot": 7
- "n": 4159681
"n_hex": "0x3f78c1"
"n_bit": "2^22 - 2^15 - 2^11 + 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 7 * 619 + 1"
"nd": 3598527
"nd_hex": "0x36e8bf"
"nd_bit": "2^22 - 2^19 - 2^16 - 2^13 + 2^11 + 2^8 - 2^6 - 1"
"r2": 764001
"r2_hex": "0xba861"
"r2_bit": "2^20 - 2^18 - 2^15 + 2^13 + 2^11 + 2^7 - 2^5 + 1"
"znprimroot": 13
- "n": 4192129
"n_hex": "0x3ff781"
"n_bit": "2^22 - 2^11 - 2^7 + 1"
"n_fac": "2^7 * 3^3 * 1213 + 1"
"nd": 1554303
"nd_hex": "0x17b77f"
"nd_bit": "2^21 - 2^19 - 2^14 - 2^11 - 2^7 - 1"
"r2": 538496
"r2_hex": "0x83780"
"r2_bit": "2^19 + 2^14 - 2^11 - 2^7"
"znprimroot": 17
- "n": 4126081
"n_hex": "0x3ef581"
"n_bit": "2^22 - 2^16 - 2^11 - 2^9 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 7 * 307 + 1"
"nd": 3192191
"nd_hex": "0x30b57f"
"nd_bit": "2^22 - 2^20 + 2^16 - 2^14 - 2^11 - 2^9 - 2^7 - 1"
"r2": 158361
"r2_hex": "0x26a99"
"r2_bit": "2^17 + 2^15 - 2^13 + 2^11 + 2^9 + 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 13
- "n": 3991681
"n_hex": "0x3ce881"
"n_bit": "2^22 - 2^18 + 2^16 - 2^13 + 2^11 + 2^7 + 1"
"n_fac": "2^7 * 3^4 * 5 * 7 * 11 + 1"
"nd": 3451007
"nd_hex": "0x34a87f"
"nd_bit": "2^22 - 2^20 + 2^18 + 2^15 + 2^13 + 2^11 + 2^7 - 1"
"r2": 1641044
"r2_hex": "0x190a54"
"r2_bit": "2^21 - 2^19 + 2^16 + 2^11 + 2^9 + 2^6 + 2^4 + 2^2"
"znprimroot": 41
- "n": 4181761
"n_hex": "0x3fcf01"
"n_bit": "2^22 - 2^14 + 2^12 - 2^8 + 1"
"n_fac": "2^8 * 3^3 * 5 * 11^2 + 1"
"nd": 2019071
"nd_hex": "0x1eceff"
"nd_bit": "2^21 - 2^16 - 2^14 + 2^12 - 2^8 - 1"
"r2": 2601692
"r2_hex": "0x27b2dc"
"r2_bit": "2^21 + 2^19 - 2^14 - 2^12 + 2^10 - 2^8 - 2^5 - 2^2"
"znprimroot": 14
- "n": 4179457
"n_hex": "0x3fc601"
"n_bit": "2^22 - 2^14 + 2^11 - 2^9 + 1"
"n_fac": "2^9 * 3^2 * 907 + 1"
"nd": 1820159
"nd_hex": "0x1bc5ff"
"nd_bit": "2^21 - 2^18 - 2^14 + 2^11 - 2^9 - 1"
"r2": 3101645
"r2_hex": "0x2f53cd"
"r2_bit": "2^22 - 2^20 - 2^16 + 2^14 + 2^12 + 2^10 - 2^6 + 2^4 - 2^2 + 1"
"znprimroot": 5
- "n": 4108801
"n_hex": "0x3eb201"
"n_bit": "2^22 - 2^16 - 2^14 - 2^12 + 2^9 + 1"
"n_fac": "2^9 * 3 * 5^2 * 107 + 1"
"nd": 3846655
"nd_hex": "0x3ab1ff"
"nd_bit": "2^22 - 2^18 - 2^16 - 2^14 - 2^12 + 2^9 - 1"
"r2": 1206030
"r2_hex": "0x12670e"
"r2_bit": "2^20 + 2^17 + 2^15 - 2^13 + 2^11 - 2^8 + 2^4 - 2"
"znprimroot": 17
- "n": 3939841
"n_hex": "0x3c1e01"
"n_bit": "2^22 - 2^18 + 2^13 - 2^9 + 1"
"n_fac": "2^9 * 3^4 * 5 * 19 + 1"
"nd": 3677695
"nd_hex": "0x381dff"
"nd_bit": "2^22 - 2^19 + 2^13 - 2^9 - 1"
"r2": 131534
"r2_hex": "0x201ce"
"r2_bit": "2^17 + 2^9 - 2^6 + 2^4 - 2"
"znprimroot": 7
- "n": 4191233
"n_hex": "0x3ff401"
"n_bit": "2^22 - 2^12 + 2^10 + 1"
"n_fac": "2^10 * 4093 + 1"
"nd": 3142655
"nd_hex": "0x2ff3ff"
"nd_bit": "2^22 - 2^20 - 2^12 + 2^10 - 1"
"r2": 1048575
"r2_hex": "0xfffff"
"r2_bit": "2^20 - 1"
"znprimroot": 3
- "n": 4187137
"n_hex": "0x3fe401"
"n_bit": "2^22 - 2^13 + 2^10 + 1"
"n_fac": "2^10 * 3 * 29 * 47 + 1"
"nd": 3138559
"nd_hex": "0x2fe3ff"
"nd_bit": "2^22 - 2^20 - 2^13 + 2^10 - 1"
"r2": 1120245
"r2_hex": "0x1117f5"
"r2_bit": "2^20 + 2^16 + 2^13 - 2^11 - 2^4 + 2^2 + 1"
"znprimroot": 5
- "n": 4188161
"n_hex": "0x3fe801"
"n_bit": "2^22 - 2^13 + 2^11 + 1"
"n_fac": "2^11 * 5 * 409 + 1"
"nd": 4188159
"nd_hex": "0x3fe7ff"
"nd_bit": "2^22 - 2^13 + 2^11 - 1"
"r2": 43000
"r2_hex": "0xa7f8"
"r2_bit": "2^15 + 2^13 + 2^11 - 2^3"
"znprimroot": 3
- "n": 4171777
"n_hex": "0x3fa801"
"n_bit": "2^22 - 2^15 + 2^13 + 2^11 + 1"
"n_fac": "2^11 * 3 * 7 * 97 + 1"
"nd": 4171775
"nd_hex": "0x3fa7ff"
"nd_bit": "2^22 - 2^15 + 2^13 + 2^11 - 1"
"r2": 2680712
"r2_hex": "0x28e788"
"r2_bit": "2^21 + 2^19 + 2^16 - 2^13 + 2^11 - 2^7 + 2^3"
"znprimroot": 5
- "n": 4085761
"n_hex": "0x3e5801"
"n_bit": "2^22 - 2^17 + 2^15 - 2^13 - 2^11 + 1"
"n_fac": "2^11 * 3 * 5 * 7 * 19 + 1"
"nd": 4085759
"nd_hex": "0x3e57ff"
"nd_bit": "2^22 - 2^17 + 2^15 - 2^13 - 2^11 - 1"
"r2": 2333886
"r2_hex": "0x239cbe"
"r2_bit": "2^21 + 2^18 - 2^15 + 2^13 - 2^10 + 2^8 - 2^6 - 2"
"znprimroot": 41
- "n": 4165633
"n_hex": "0x3f9001"
"n_bit": "2^22 - 2^15 + 2^12 + 1"
"n_fac": "2^12 * 3^2 * 113 + 1"
"nd": 4165631
"nd_hex": "0x3f8fff"
"nd_bit": "2^22 - 2^15 + 2^12 - 1"
"r2": 1396540
"r2_hex": "0x154f3c"
"r2_bit": "2^20 + 2^18 + 2^16 + 2^14 + 2^12 - 2^8 + 2^6 - 2^2"
"znprimroot": 5
- "n": 3993601
"n_hex": "0x3cf001"
"n_bit": "2^22 - 2^18 + 2^16 - 2^12 + 1"
"n_fac": "2^12 * 3 * 5^2 * 13 + 1"
"nd": 3993599
"nd_hex": "0x3cefff"
"nd_bit": "2^22 - 2^18 + 2^16 - 2^12 - 1"
"r2": 2234523
"r2_hex": "0x22189b"
"r2_bit": "2^21 + 2^17 + 2^13 - 2^11 + 2^7 + 2^5 - 2^2 - 1"
"znprimroot": 11
- "n": 3870721
"n_hex": "0x3b1001"
"n_bit": "2^22 - 2^18 - 2^16 + 2^12 + 1"
"n_fac": "2^12 * 3^3 * 5 * 7 + 1"
"nd": 3870719
"nd_hex": "0x3b0fff"
"nd_bit": "2^22 - 2^18 - 2^16 + 2^12 - 1"
"r2": 2954839
"r2_hex": "0x2d1657"
"r2_bit": "2^22 - 2^20 - 2^18 + 2^16 + 2^13 - 2^11 - 2^9 + 2^7 - 2^5 - 2^3 - 1"
"znprimroot": 41
- "n": 4169729
"n_hex": "0x3fa001"
"n_bit": "2^22 - 2^15 + 2^13 + 1"
"n_fac": "2^13 * 509 + 1"
"nd": 4169727
"nd_hex": "0x3f9fff"
"nd_bit": "2^22 - 2^15 + 2^13 - 1"
"r2": 3489649
"r2_hex": "0x353f71"
"r2_bit": "2^22 - 2^20 + 2^18 + 2^16 + 2^14 - 2^7 - 2^4 + 1"
"znprimroot": 3
- "n": 4104193
"n_hex": "0x3ea001"
"n_bit": "2^22 - 2^17 + 2^15 + 2^13 + 1"
"n_fac": "2^13 * 3 * 167 + 1"
"nd": 4104191
"nd_hex": "0x3e9fff"
"nd_bit": "2^22 - 2^17 + 2^15 + 2^13 - 1"
"r2": 1898567
"r2_hex": "0x1cf847"
"r2_bit": "2^21 - 2^18 + 2^16 - 2^11 + 2^6 + 2^3 - 1"
"znprimroot": 5
- "n": 4079617
"n_hex": "0x3e4001"
"n_bit": "2^22 - 2^17 + 2^14 + 1"
"n_fac": "2^14 * 3 * 83 + 1"
"nd": 4079615
"nd_hex": "0x3e3fff"
"nd_bit": "2^22 - 2^17 + 2^14 - 1"
"r2": 422761
"r2_hex": "0x67369"
"r2_bit": "2^19 - 2^17 + 2^15 - 2^12 + 2^10 - 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 5
- "n": 3686401
"n_hex": "0x384001"
"n_bit": "2^22 - 2^19 + 2^14 + 1"
"n_fac": "2^14 * 3^2 * 5^2 + 1"
"nd": 3686399
"nd_hex": "0x383fff"
"nd_bit": "2^22 - 2^19 + 2^14 - 1"
"r2": 2174632
"r2_hex": "0x212ea8"
"r2_bit": "2^21 + 2^16 + 2^14 - 2^12 - 2^9 + 2^7 + 2^5 + 2^3"
"znprimroot": 14
- "n": 1720321
"n_hex": "0x1a4001"
"n_bit": "2^21 - 2^19 + 2^17 + 2^14 + 1"
"n_fac": "2^14 * 3 * 5 * 7 + 1"
"nd": 1720319
"nd_hex": "0x1a3fff"
"nd_bit": "2^21 - 2^19 + 2^17 + 2^14 - 1"
"r2": 1144390
"r2_hex": "0x117646"
"r2_bit": "2^20 + 2^17 - 2^15 - 2^11 - 2^9 + 2^6 + 2^3 - 2"
"znprimroot": 17
- "n": 2654209
"n_hex": "0x288001"
"n_bit": "2^21 + 2^19 + 2^15 + 1"
"n_fac": "2^15 * 3^4 + 1"
"nd": 2654207
"nd_hex": "0x287fff"
"nd_bit": "2^21 + 2^19 + 2^15 - 1"
"r2": 1203519
"r2_hex": "0x125d3f"
"r2_bit": "2^20 + 2^17 + 2^15 - 2^13 - 2^10 + 2^8 + 2^6 - 1"
"znprimroot": 11
- "n": 3735553
"n_hex": "0x390001"
"n_bit": "2^22 - 2^19 + 2^16 + 1"
"n_fac": "2^16 * 3 * 19 + 1"
"nd": 3735551
"nd_hex": "0x38ffff"
"nd_bit": "2^22 - 2^19 + 2^16 - 1"
"r2": 2630640
"r2_hex": "0x2823f0"
"r2_bit": "2^21 + 2^19 + 2^13 + 2^10 - 2^4"
"znprimroot": 5
- "n": 1769473
"n_hex": "0x1b0001"
"n_bit": "2^21 - 2^18 - 2^16 + 1"
"n_fac": "2^16 * 3^3 + 1"
"nd": 1769471
"nd_hex": "0x1affff"
"nd_bit": "2^21 - 2^18 - 2^16 - 1"
"r2": 543712
"r2_hex": "0x84be0"
"r2_bit": "2^19 + 2^14 + 2^12 - 2^10 - 2^5"
"znprimroot": 5
- "n": 2752513
"n_hex": "0x2a0001"
"n_bit": "2^21 + 2^19 + 2^17 + 1"
"n_fac": "2^17 * 3 * 7 + 1"
"nd": 2752511
"nd_hex": "0x29ffff"
"nd_bit": "2^21 + 2^19 + 2^17 - 1"
"r2": 162282
"r2_hex": "0x279ea"
"r2_bit": "2^17 + 2^15 - 2^11 + 2^9 - 2^5 + 2^3 + 2"
"znprimroot": 20
- "n": 1179649
"n_hex": "0x120001"
"n_bit": "2^20 + 2^17 + 1"
"n_fac": "2^17 * 3^2 + 1"
"nd": 1179647
"nd_hex": "0x11ffff"
"nd_bit": "2^20 + 2^17 - 1"
"r2": 291284
"r2_hex": "0x471d4"
"r2_bit": "2^18 + 2^15 - 2^12 + 2^9 - 2^6 + 2^4 + 2^2"
"znprimroot": 19
- "n": 786433
"n_hex": "0xc0001"
"n_bit": "2^20 - 2^18 + 1"
"n_fac": "2^18 * 3 + 1"
"nd": 786431
"nd_hex": "0xbffff"
"nd_bit": "2^20 - 2^18 - 1"
"r2": 699080
"r2_hex": "0xaaac8"
"r2_bit": "2^20 - 2^18 - 2^16 - 2^14 - 2^12 - 2^10 - 2^8 - 2^6 + 2^3"
"znprimroot": 10
Raw
result_prime_0023.yaml
- "r": 23
"primes":
- "n": 8388571
"n_hex": "0x7fffdb"
"n_bit": "2^23 - 2^5 - 2^2 - 1"
"n_fac": "2 * 3 * 5 * 279619 + 1"
"nd": 4987821
"nd_hex": "0x4c1bad"
"nd_bit": "2^22 + 2^20 - 2^18 + 2^13 - 2^10 - 2^6 - 2^4 - 2^2 + 1"
"r2": 1369
"r2_hex": "0x559"
"r2_bit": "2^11 - 2^9 - 2^7 - 2^5 - 2^3 + 1"
"znprimroot": 3
- "n": 8388451
"n_hex": "0x7fff63"
"n_bit": "2^23 - 2^7 - 2^5 + 2^2 - 1"
"n_fac": "2 * 3^2 * 5^2 * 7 * 2663 + 1"
"nd": 427445
"nd_hex": "0x685b5"
"nd_bit": "2^19 - 2^17 + 2^15 + 2^11 - 2^9 - 2^6 - 2^4 + 2^2 + 1"
"r2": 24649
"r2_hex": "0x6049"
"r2_bit": "2^15 - 2^13 + 2^6 + 2^3 + 1"
"znprimroot": 3
- "n": 8388421
"n_hex": "0x7fff45"
"n_bit": "2^23 - 2^8 + 2^6 + 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 251 * 557 + 1"
"nd": 672883
"nd_hex": "0xa4473"
"nd_bit": "2^19 + 2^17 + 2^14 + 2^10 + 2^7 - 2^4 + 2^2 - 1"
"r2": 34969
"r2_hex": "0x8899"
"r2_bit": "2^15 + 2^11 + 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 8388109
"n_hex": "0x7ffe0d"
"n_bit": "2^23 - 2^9 + 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 41 * 5683 + 1"
"nd": 5799739
"nd_hex": "0x587f3b"
"nd_bit": "2^23 - 2^21 - 2^19 + 2^15 - 2^8 + 2^6 - 2^2 - 1"
"r2": 249001
"r2_hex": "0x3cca9"
"r2_bit": "2^18 - 2^14 + 2^12 - 2^10 + 2^7 + 2^5 + 2^3 + 1"
"znprimroot": 6
- "n": 8387101
"n_hex": "0x7ffa1d"
"n_bit": "2^23 - 2^11 + 2^9 + 2^5 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5^2 * 9319 + 1"
"nd": 8349643
"nd_hex": "0x7f67cb"
"nd_bit": "2^23 - 2^15 - 2^13 + 2^11 - 2^6 + 2^4 - 2^2 - 1"
"r2": 2271049
"r2_hex": "0x22a749"
"r2_bit": "2^21 + 2^17 + 2^15 + 2^13 + 2^11 - 2^8 + 2^6 + 2^3 + 1"
"znprimroot": 6
- "n": 8386141
"n_hex": "0x7ff65d"
"n_bit": "2^23 - 2^11 - 2^9 + 2^7 - 2^5 - 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 7 * 41 * 487 + 1"
"nd": 4682251
"nd_hex": "0x47720b"
"nd_bit": "2^22 + 2^19 - 2^15 - 2^12 + 2^9 + 2^4 - 2^2 - 1"
"r2": 6086089
"r2_hex": "0x5cddc9"
"r2_bit": "2^23 - 2^21 - 2^18 + 2^16 - 2^13 - 2^9 - 2^6 + 2^3 + 1"
"znprimroot": 14
- "n": 8388409
"n_hex": "0x7fff39"
"n_bit": "2^23 - 2^8 + 2^6 - 2^3 + 1"
"n_fac": "2^3 * 3 * 7^3 * 1019 + 1"
"nd": 4636919
"nd_hex": "0x46c0f7"
"nd_bit": "2^22 + 2^19 - 2^16 - 2^14 + 2^8 - 2^3 - 1"
"r2": 39601
"r2_hex": "0x9ab1"
"r2_bit": "2^15 + 2^13 - 2^10 - 2^8 - 2^6 - 2^4 + 1"
"znprimroot": 11
- "n": 8386921
"n_hex": "0x7ff969"
"n_bit": "2^23 - 2^11 + 2^9 - 2^7 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5 * 23297 + 1"
"nd": 8378663
"nd_hex": "0x7fd927"
"nd_bit": "2^23 - 2^13 - 2^11 + 2^8 + 2^5 + 2^3 - 1"
"r2": 2845969
"r2_hex": "0x2b6d11"
"r2_bit": "2^22 - 2^20 - 2^18 - 2^15 - 2^12 - 2^10 + 2^8 + 2^4 + 1"
"znprimroot": 17
- "n": 8385721
"n_hex": "0x7ff4b9"
"n_bit": "2^23 - 2^12 + 2^10 + 2^8 - 2^6 - 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 7 * 67 * 149 + 1"
"nd": 7089783
"nd_hex": "0x6c2e77"
"nd_bit": "2^23 - 2^20 - 2^18 + 2^14 - 2^12 - 2^9 + 2^7 - 2^3 - 1"
"r2": 8334769
"r2_hex": "0x7f2db1"
"r2_bit": "2^23 - 2^16 + 2^14 - 2^12 - 2^9 - 2^6 - 2^4 + 1"
"znprimroot": 19
- "n": 8384041
"n_hex": "0x7fee29"
"n_bit": "2^23 - 2^12 - 2^9 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^3 * 5 * 7 * 1109 + 1"
"nd": 7369191
"nd_hex": "0x7071e7"
"nd_bit": "2^23 - 2^20 + 2^15 - 2^12 + 2^9 - 2^5 + 2^3 - 1"
"r2": 4089407
"r2_hex": "0x3e663f"
"r2_bit": "2^22 - 2^17 + 2^15 - 2^13 + 2^11 - 2^9 + 2^6 - 1"
"znprimroot": 11
- "n": 8388593
"n_hex": "0x7ffff1"
"n_bit": "2^23 - 2^4 + 1"
"n_fac": "2^4 * 524287 + 1"
"nd": 7270127
"nd_hex": "0x6eeeef"
"nd_bit": "2^23 - 2^20 - 2^16 - 2^12 - 2^8 - 2^4 - 1"
"r2": 225
"r2_hex": "0xe1"
"r2_bit": "2^8 - 2^5 + 1"
"znprimroot": 3
- "n": 8387857
"n_hex": "0x7ffd11"
"n_bit": "2^23 - 2^10 + 2^8 + 2^4 + 1"
"n_fac": "2^4 * 3^2 * 31 * 1879 + 1"
"nd": 7171087
"nd_hex": "0x6d6c0f"
"nd_bit": "2^23 - 2^20 - 2^17 - 2^15 - 2^12 - 2^10 + 2^4 - 1"
"r2": 564001
"r2_hex": "0x89b21"
"r2_bit": "2^19 + 2^15 + 2^13 - 2^10 - 2^8 + 2^5 + 1"
"znprimroot": 5
- "n": 8384881
"n_hex": "0x7ff171"
"n_bit": "2^23 - 2^12 + 2^9 - 2^7 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5 * 7^2 * 23 * 31 + 1"
"nd": 4411503
"nd_hex": "0x43506f"
"nd_bit": "2^22 + 2^18 - 2^16 + 2^14 + 2^12 + 2^7 - 2^4 - 1"
"r2": 5505648
"r2_hex": "0x540270"
"r2_bit": "2^22 + 2^20 + 2^18 + 2^9 + 2^7 - 2^4"
"znprimroot": 17
- "n": 8384401
"n_hex": "0x7fef91"
"n_bit": "2^23 - 2^12 - 2^7 + 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5^2 * 17 * 137 + 1"
"nd": 5983887
"nd_hex": "0x5b4e8f"
"nd_bit": "2^23 - 2^21 - 2^18 - 2^16 + 2^14 + 2^12 - 2^9 + 2^7 + 2^4 - 1"
"r2": 930047
"r2_hex": "0xe30ff"
"r2_bit": "2^20 - 2^17 + 2^14 - 2^12 + 2^8 - 1"
"znprimroot": 31
- "n": 8388449
"n_hex": "0x7fff61"
"n_bit": "2^23 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 262139 + 1"
"nd": 3218271
"nd_hex": "0x311b5f"
"nd_bit": "2^22 - 2^20 + 2^16 + 2^13 - 2^10 - 2^7 - 2^5 - 1"
"r2": 25281
"r2_hex": "0x62c1"
"r2_bit": "2^15 - 2^13 + 2^10 - 2^8 - 2^6 + 1"
"znprimroot": 3
- "n": 8387809
"n_hex": "0x7ffce1"
"n_bit": "2^23 - 2^10 + 2^8 - 2^5 + 1"
"n_fac": "2^5 * 3 * 11 * 13^2 * 47 + 1"
"nd": 6404319
"nd_hex": "0x61b8df"
"nd_bit": "2^23 - 2^21 + 2^17 - 2^14 - 2^11 + 2^8 - 2^5 - 1"
"r2": 638401
"r2_hex": "0x9bdc1"
"r2_bit": "2^19 + 2^17 - 2^14 - 2^9 - 2^6 + 1"
"znprimroot": 7
- "n": 8382529
"n_hex": "0x7fe841"
"n_bit": "2^23 - 2^13 + 2^11 + 2^6 + 1"
"n_fac": "2^6 * 3^5 * 7^2 * 11 + 1"
"nd": 5232703
"nd_hex": "0x4fd83f"
"nd_bit": "2^22 + 2^20 - 2^13 - 2^11 + 2^6 - 1"
"r2": 3424125
"r2_hex": "0x343f7d"
"r2_bit": "2^22 - 2^20 + 2^18 + 2^14 - 2^7 - 2^2 + 1"
"znprimroot": 19
- "n": 8377921
"n_hex": "0x7fd641"
"n_bit": "2^23 - 2^13 - 2^11 - 2^9 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 2909 + 1"
"nd": 5555775
"nd_hex": "0x54c63f"
"nd_bit": "2^22 + 2^20 + 2^18 + 2^16 - 2^14 + 2^11 - 2^9 + 2^6 - 1"
"r2": 5298996
"r2_hex": "0x50db34"
"r2_bit": "2^22 + 2^20 + 2^16 - 2^13 - 2^10 - 2^8 + 2^6 - 2^4 + 2^2"
"znprimroot": 21
- "n": 8366401
"n_hex": "0x7fa941"
"n_bit": "2^23 - 2^15 + 2^13 + 2^11 + 2^8 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5^2 * 7 * 83 + 1"
"nd": 923967
"nd_hex": "0xe193f"
"nd_bit": "2^20 - 2^17 + 2^13 - 2^11 + 2^8 + 2^6 - 1"
"r2": 7899591
"r2_hex": "0x7889c7"
"r2_bit": "2^23 - 2^19 + 2^15 + 2^11 + 2^9 - 2^6 + 2^3 - 1"
"znprimroot": 29
- "n": 8386177
"n_hex": "0x7ff681"
"n_bit": "2^23 - 2^11 - 2^9 + 2^7 + 1"
"n_fac": "2^7 * 3 * 21839 + 1"
"nd": 4568703
"nd_hex": "0x45b67f"
"nd_bit": "2^22 + 2^19 - 2^17 - 2^14 - 2^11 - 2^9 + 2^7 - 1"
"r2": 5909761
"r2_hex": "0x5a2d01"
"r2_bit": "2^23 - 2^21 - 2^19 + 2^17 + 2^14 - 2^12 - 2^10 + 2^8 + 1"
"znprimroot": 5
- "n": 8384641
"n_hex": "0x7ff081"
"n_bit": "2^23 - 2^12 + 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 11 * 397 + 1"
"nd": 3125375
"nd_hex": "0x2fb07f"
"nd_bit": "2^22 - 2^20 - 2^14 - 2^12 + 2^7 - 1"
"r2": 7352448
"r2_hex": "0x703080"
"r2_bit": "2^23 - 2^20 + 2^14 - 2^12 + 2^7"
"znprimroot": 7
- "n": 8346241
"n_hex": "0x7f5a81"
"n_bit": "2^23 - 2^15 - 2^13 - 2^11 + 2^9 + 2^7 + 1"
"n_fac": "2^7 * 3^4 * 5 * 7 * 23 + 1"
"nd": 2169471
"nd_hex": "0x211a7f"
"nd_bit": "2^21 + 2^16 + 2^13 - 2^11 + 2^9 + 2^7 - 1"
"r2": 520874
"r2_hex": "0x7f2aa"
"r2_bit": "2^19 - 2^12 + 2^9 + 2^7 + 2^5 + 2^3 + 2"
"znprimroot": 26
- "n": 8386817
"n_hex": "0x7ff901"
"n_bit": "2^23 - 2^11 + 2^8 + 1"
"n_fac": "2^8 * 181^2 + 1"
"nd": 5175551
"nd_hex": "0x4ef8ff"
"nd_bit": "2^22 + 2^20 - 2^16 - 2^11 + 2^8 - 1"
"r2": 3207681
"r2_hex": "0x30f201"
"r2_bit": "2^22 - 2^20 + 2^16 - 2^12 + 2^9 + 1"
"znprimroot": 3
- "n": 8375041
"n_hex": "0x7fcb01"
"n_bit": "2^23 - 2^14 + 2^12 - 2^10 - 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5 * 727 + 1"
"nd": 445183
"nd_hex": "0x6caff"
"nd_bit": "2^19 - 2^16 - 2^14 + 2^12 - 2^10 - 2^8 - 1"
"r2": 8187628
"r2_hex": "0x7ceeec"
"r2_bit": "2^23 - 2^18 + 2^16 - 2^12 - 2^8 - 2^4 - 2^2"
"znprimroot": 19
- "n": 8144641
"n_hex": "0x7c4701"
"n_bit": "2^23 - 2^18 + 2^14 + 2^11 - 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5 * 7 * 101 + 1"
"nd": 4933375
"nd_hex": "0x4b46ff"
"nd_bit": "2^22 + 2^20 - 2^18 - 2^16 + 2^14 + 2^11 - 2^8 - 1"
"r2": 7005302
"r2_hex": "0x6ae476"
"r2_bit": "2^23 - 2^20 - 2^18 - 2^16 - 2^13 + 2^10 + 2^7 - 2^3 - 2"
"znprimroot": 26
- "n": 8372737
"n_hex": "0x7fc201"
"n_bit": "2^23 - 2^14 + 2^9 + 1"
"n_fac": "2^9 * 3^2 * 23 * 79 + 1"
"nd": 8110591
"nd_hex": "0x7bc1ff"
"nd_bit": "2^23 - 2^18 - 2^14 + 2^9 - 1"
"r2": 706531
"r2_hex": "0xac7e3"
"r2_bit": "2^20 - 2^18 - 2^16 - 2^14 + 2^11 - 2^5 + 2^2 - 1"
"znprimroot": 5
- "n": 8117761
"n_hex": "0x7bde01"
"n_bit": "2^23 - 2^18 - 2^13 - 2^9 + 1"
"n_fac": "2^9 * 3 * 5 * 7 * 151 + 1"
"nd": 7855615
"nd_hex": "0x77ddff"
"nd_bit": "2^23 - 2^19 - 2^13 - 2^9 - 1"
"r2": 6009013
"r2_hex": "0x5bb0b5"
"r2_bit": "2^23 - 2^21 - 2^18 - 2^14 - 2^12 + 2^8 - 2^6 - 2^4 + 2^2 + 1"
"znprimroot": 26
- "n": 8383489
"n_hex": "0x7fec01"
"n_bit": "2^23 - 2^12 - 2^10 + 1"
"n_fac": "2^10 * 3 * 2729 + 1"
"nd": 7334911
"nd_hex": "0x6febff"
"nd_bit": "2^23 - 2^20 - 2^12 - 2^10 - 1"
"r2": 1053694
"r2_hex": "0x1013fe"
"r2_bit": "2^20 + 2^12 + 2^10 - 2"
"znprimroot": 17
- "n": 8309761
"n_hex": "0x7ecc01"
"n_bit": "2^23 - 2^16 - 2^14 + 2^12 - 2^10 + 1"
"n_fac": "2^10 * 3 * 5 * 541 + 1"
"nd": 7261183
"nd_hex": "0x6ecbff"
"nd_bit": "2^23 - 2^20 - 2^16 - 2^14 + 2^12 - 2^10 - 1"
"r2": 1148181
"r2_hex": "0x118515"
"r2_bit": "2^20 + 2^17 - 2^15 + 2^10 + 2^8 + 2^4 + 2^2 + 1"
"znprimroot": 13
- "n": 8248321
"n_hex": "0x7ddc01"
"n_bit": "2^23 - 2^17 - 2^13 - 2^10 + 1"
"n_fac": "2^10 * 3^2 * 5 * 179 + 1"
"nd": 7199743
"nd_hex": "0x6ddbff"
"nd_bit": "2^23 - 2^20 - 2^17 - 2^13 - 2^10 - 1"
"r2": 8196784
"r2_hex": "0x7d12b0"
"r2_bit": "2^23 - 2^18 + 2^16 + 2^12 + 2^10 - 2^8 - 2^6 - 2^4"
"znprimroot": 34
- "n": 7848961
"n_hex": "0x77c401"
"n_bit": "2^23 - 2^19 - 2^14 + 2^10 + 1"
"n_fac": "2^10 * 3 * 5 * 7 * 73 + 1"
"nd": 6800383
"nd_hex": "0x67c3ff"
"nd_bit": "2^23 - 2^21 + 2^19 - 2^14 + 2^10 - 1"
"r2": 6733587
"r2_hex": "0x66bf13"
"r2_bit": "2^23 - 2^21 + 2^19 - 2^16 - 2^14 - 2^8 + 2^4 + 2^2 - 1"
"znprimroot": 17
- "n": 7925761
"n_hex": "0x78f001"
"n_bit": "2^23 - 2^19 + 2^16 - 2^12 + 1"
"n_fac": "2^12 * 3^2 * 5 * 43 + 1"
"nd": 7925759
"nd_hex": "0x78efff"
"nd_bit": "2^23 - 2^19 + 2^16 - 2^12 - 1"
"r2": 1951340
"r2_hex": "0x1dc66c"
"r2_bit": "2^21 - 2^17 - 2^14 + 2^11 - 2^9 + 2^7 - 2^4 - 2^2"
"znprimroot": 11
- "n": 8380417
"n_hex": "0x7fe001"
"n_bit": "2^23 - 2^13 + 1"
"n_fac": "2^13 * 3 * 11 * 31 + 1"
"nd": 8380415
"nd_hex": "0x7fdfff"
"nd_bit": "2^23 - 2^13 - 1"
"r2": 49145
"r2_hex": "0xbff9"
"r2_bit": "2^16 - 2^14 - 2^3 + 1"
"znprimroot": 10
- "n": 7741441
"n_hex": "0x762001"
"n_bit": "2^23 - 2^19 - 2^17 + 2^13 + 1"
"n_fac": "2^13 * 3^3 * 5 * 7 + 1"
"nd": 7741439
"nd_hex": "0x761fff"
"nd_bit": "2^23 - 2^19 - 2^17 + 2^13 - 1"
"r2": 5426348
"r2_hex": "0x52ccac"
"r2_bit": "2^22 + 2^20 + 2^18 - 2^16 - 2^14 + 2^12 - 2^10 + 2^8 - 2^6 - 2^4 - 2^2"
"znprimroot": 26
- "n": 8273921
"n_hex": "0x7e4001"
"n_bit": "2^23 - 2^17 + 2^14 + 1"
"n_fac": "2^14 * 5 * 101 + 1"
"nd": 8273919
"nd_hex": "0x7e3fff"
"nd_bit": "2^23 - 2^17 + 2^14 - 1"
"r2": 5847500
"r2_hex": "0x5939cc"
"r2_bit": "2^23 - 2^21 - 2^19 + 2^16 + 2^14 - 2^11 + 2^9 - 2^6 + 2^4 - 2^2"
"znprimroot": 6
- "n": 6635521
"n_hex": "0x654001"
"n_bit": "2^23 - 2^21 + 2^18 + 2^16 + 2^14 + 1"
"n_fac": "2^14 * 3^4 * 5 + 1"
"nd": 6635519
"nd_hex": "0x653fff"
"nd_bit": "2^23 - 2^21 + 2^18 + 2^16 + 2^14 - 1"
"r2": 6123209
"r2_hex": "0x5d6ec9"
"r2_bit": "2^23 - 2^21 - 2^17 - 2^15 - 2^12 - 2^8 - 2^6 + 2^3 + 1"
"znprimroot": 19
- "n": 1720321
"n_hex": "0x1a4001"
"n_bit": "2^21 - 2^19 + 2^17 + 2^14 + 1"
"n_fac": "2^14 * 3 * 5 * 7 + 1"
"nd": 1720319
"nd_hex": "0x1a3fff"
"nd_bit": "2^21 - 2^19 + 2^17 + 2^14 - 1"
"r2": 1136918
"r2_hex": "0x115916"
"r2_bit": "2^20 + 2^17 - 2^15 - 2^13 - 2^11 + 2^8 + 2^5 - 2^3 - 2"
"znprimroot": 17
- "n": 4423681
"n_hex": "0x438001"
"n_bit": "2^22 + 2^18 - 2^15 + 1"
"n_fac": "2^15 * 3^3 * 5 + 1"
"nd": 4423679
"nd_hex": "0x437fff"
"nd_bit": "2^22 + 2^18 - 2^15 - 1"
"r2": 3032622
"r2_hex": "0x2e462e"
"r2_bit": "2^22 - 2^20 - 2^17 + 2^14 + 2^11 - 2^9 + 2^6 - 2^4 - 2"
"znprimroot": 14
- "n": 8257537
"n_hex": "0x7e0001"
"n_bit": "2^23 - 2^17 + 1"
"n_fac": "2^17 * 3^2 * 7 + 1"
"nd": 8257535
"nd_hex": "0x7dffff"
"nd_bit": "2^23 - 2^17 - 1"
"r2": 3930081
"r2_hex": "0x3bf7e1"
"r2_bit": "2^22 - 2^18 - 2^11 - 2^5 + 1"
"znprimroot": 5
- "n": 786433
"n_hex": "0xc0001"
"n_bit": "2^20 - 2^18 + 1"
"n_fac": "2^18 * 3 + 1"
"nd": 786431
"nd_hex": "0xbffff"
"nd_bit": "2^20 - 2^18 - 1"
"r2": 437021
"r2_hex": "0x6ab1d"
"r2_bit": "2^19 - 2^16 - 2^14 - 2^12 - 2^10 - 2^8 + 2^5 - 2^2 + 1"
"znprimroot": 10
- "n": 7340033
"n_hex": "0x700001"
"n_bit": "2^23 - 2^20 + 1"
"n_fac": "2^20 * 7 + 1"
"nd": 7340031
"nd_hex": "0x6fffff"
"nd_bit": "2^23 - 2^20 - 1"
"r2": 1947357
"r2_hex": "0x1db6dd"
"r2_bit": "2^21 - 2^17 - 2^14 - 2^11 - 2^8 - 2^5 - 2^2 + 1"
"znprimroot": 3
Raw
result_prime_0024.yaml
- "r": 24
"primes":
- "n": 16777213
"n_hex": "0xfffffd"
"n_bit": "2^24 - 2^2 + 1"
"n_fac": "2^2 * 3 * 23 * 89 * 683 + 1"
"nd": 11184811
"nd_hex": "0xaaaaab"
"nd_bit": "2^24 - 2^22 - 2^20 - 2^18 - 2^16 - 2^14 - 2^12 - 2^10 - 2^8 - 2^6 - 2^4 - 2^2 - 1"
"r2": 9
"r2_hex": "0x9"
"r2_bit": "2^3 + 1"
"znprimroot": 5
- "n": 16777141
"n_hex": "0xffffb5"
"n_bit": "2^24 - 2^6 - 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 279619 + 1"
"nd": 3131747
"nd_hex": "0x2fc963"
"nd_bit": "2^22 - 2^20 - 2^14 + 2^11 + 2^9 - 2^7 - 2^5 + 2^2 - 1"
"r2": 5625
"r2_hex": "0x15f9"
"r2_bit": "2^13 - 2^11 - 2^9 - 2^3 + 1"
"znprimroot": 6
- "n": 16776901
"n_hex": "0xfffec5"
"n_bit": "2^24 - 2^8 - 2^6 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5^2 * 7 * 2663 + 1"
"nd": 16723955
"nd_hex": "0xff2ff3"
"nd_bit": "2^24 - 2^16 + 2^14 - 2^12 - 2^4 + 2^2 - 1"
"r2": 99225
"r2_hex": "0x18399"
"r2_bit": "2^17 - 2^15 + 2^10 - 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 6
- "n": 16770601
"n_hex": "0xffe629"
"n_bit": "2^24 - 2^13 + 2^11 - 2^9 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5^2 * 7 * 11^3 + 1"
"nd": 3992039
"nd_hex": "0x3ce9e7"
"nd_bit": "2^22 - 2^18 + 2^16 - 2^13 + 2^11 + 2^9 - 2^5 + 2^3 - 1"
"r2": 10217023
"r2_hex": "0x9be63f"
"r2_bit": "2^23 + 2^21 - 2^18 - 2^13 + 2^11 - 2^9 + 2^6 - 1"
"znprimroot": 58
- "n": 16775281
"n_hex": "0xfff871"
"n_bit": "2^24 - 2^11 + 2^7 - 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5 * 23 * 1013 + 1"
"nd": 5453679
"nd_hex": "0x53376f"
"nd_bit": "2^22 + 2^20 + 2^18 - 2^16 + 2^14 - 2^11 - 2^7 - 2^4 - 1"
"r2": 3744225
"r2_hex": "0x3921e1"
"r2_bit": "2^22 - 2^19 + 2^16 + 2^13 + 2^9 - 2^5 + 1"
"znprimroot": 11
- "n": 16776481
"n_hex": "0xfffd21"
"n_bit": "2^24 - 2^10 + 2^8 + 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 7 * 4993 + 1"
"nd": 2373919
"nd_hex": "0x24391f"
"nd_bit": "2^21 + 2^18 + 2^14 - 2^11 + 2^8 + 2^5 - 1"
"r2": 540225
"r2_hex": "0x83e41"
"r2_bit": "2^19 + 2^14 - 2^9 + 2^6 + 1"
"znprimroot": 19
- "n": 16771681
"n_hex": "0xffea61"
"n_bit": "2^24 - 2^13 + 2^11 + 2^9 + 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 19 * 613 + 1"
"nd": 6407775
"nd_hex": "0x61c65f"
"nd_bit": "2^23 - 2^21 + 2^17 - 2^14 + 2^11 - 2^9 + 2^7 - 2^5 - 1"
"r2": 13864544
"r2_hex": "0xd38e60"
"r2_bit": "2^24 - 2^22 + 2^20 + 2^18 - 2^15 + 2^12 - 2^9 + 2^7 - 2^5"
"znprimroot": 7
- "n": 16763041
"n_hex": "0xffc8a1"
"n_bit": "2^24 - 2^14 + 2^11 + 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 7 * 1663 + 1"
"nd": 9692319
"nd_hex": "0x93e49f"
"nd_bit": "2^23 + 2^20 + 2^18 - 2^13 + 2^10 + 2^7 + 2^5 - 1"
"r2": 16537174
"r2_hex": "0xfc5656"
"r2_bit": "2^24 - 2^18 + 2^15 - 2^13 - 2^11 - 2^9 + 2^7 - 2^5 - 2^3 - 2"
"znprimroot": 23
- "n": 16777153
"n_hex": "0xffffc1"
"n_bit": "2^24 - 2^6 + 1"
"n_fac": "2^6 * 3^3 * 7 * 19 * 73 + 1"
"nd": 16510911
"nd_hex": "0xfbefbf"
"nd_bit": "2^24 - 2^18 - 2^12 - 2^6 - 1"
"r2": 3969
"r2_hex": "0xf81"
"r2_bit": "2^12 - 2^7 + 1"
"znprimroot": 5
- "n": 16764481
"n_hex": "0xffce41"
"n_bit": "2^24 - 2^14 + 2^12 - 2^9 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 5821 + 1"
"nd": 16301631
"nd_hex": "0xf8be3f"
"nd_bit": "2^24 - 2^19 + 2^16 - 2^14 - 2^9 + 2^6 - 1"
"r2": 11299896
"r2_hex": "0xac6c38"
"r2_bit": "2^24 - 2^22 - 2^20 - 2^18 + 2^15 - 2^12 - 2^10 + 2^6 - 2^3"
"znprimroot": 13
- "n": 16672321
"n_hex": "0xfe6641"
"n_bit": "2^24 - 2^17 + 2^15 - 2^13 + 2^11 - 2^9 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 7 * 827 + 1"
"nd": 4937279
"nd_hex": "0x4b563f"
"nd_bit": "2^22 + 2^20 - 2^18 - 2^15 - 2^13 - 2^11 - 2^9 + 2^6 - 1"
"r2": 15901486
"r2_hex": "0xf2a32e"
"r2_bit": "2^24 - 2^20 + 2^17 + 2^15 + 2^13 + 2^10 - 2^8 + 2^6 - 2^4 - 2"
"znprimroot": 22
- "n": 16774273
"n_hex": "0xfff481"
"n_bit": "2^24 - 2^12 + 2^10 + 2^7 + 1"
"n_fac": "2^7 * 3^2 * 14561 + 1"
"nd": 10204287
"nd_hex": "0x9bb47f"
"nd_bit": "2^23 + 2^21 - 2^18 - 2^14 - 2^12 + 2^10 + 2^7 - 1"
"r2": 8661249
"r2_hex": "0x842901"
"r2_bit": "2^23 + 2^18 + 2^13 + 2^11 + 2^8 + 1"
"znprimroot": 10
- "n": 16759681
"n_hex": "0xffbb81"
"n_bit": "2^24 - 2^14 - 2^10 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 7 * 29 * 43 + 1"
"nd": 9141119
"nd_hex": "0x8b7b7f"
"nd_bit": "2^23 + 2^20 - 2^18 - 2^15 - 2^10 - 2^7 - 1"
"r2": 5801967
"r2_hex": "0x5887ef"
"r2_bit": "2^23 - 2^21 - 2^19 + 2^15 + 2^11 - 2^4 - 1"
"znprimroot": 37
- "n": 16776961
"n_hex": "0xffff01"
"n_bit": "2^24 - 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 17 * 257 + 1"
"nd": 16711423
"nd_hex": "0xfefeff"
"nd_bit": "2^24 - 2^16 - 2^8 - 1"
"r2": 65025
"r2_hex": "0xfe01"
"r2_bit": "2^16 - 2^9 + 1"
"znprimroot": 7
- "n": 16768513
"n_hex": "0xffde01"
"n_bit": "2^24 - 2^13 - 2^9 + 1"
"n_fac": "2^9 * 3^3 * 1213 + 1"
"nd": 8117759
"nd_hex": "0x7bddff"
"nd_bit": "2^23 - 2^18 - 2^13 - 2^9 - 1"
"r2": 8668157
"r2_hex": "0x8443fd"
"r2_bit": "2^23 + 2^18 + 2^14 + 2^10 - 2^2 + 1"
"znprimroot": 7
- "n": 16611841
"n_hex": "0xfd7a01"
"n_bit": "2^24 - 2^17 - 2^15 - 2^11 + 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5 * 7 * 103 + 1"
"nd": 14252543
"nd_hex": "0xd979ff"
"nd_bit": "2^24 - 2^21 - 2^19 + 2^17 - 2^15 - 2^11 + 2^9 - 1"
"r2": 5800339
"r2_hex": "0x588193"
"r2_bit": "2^23 - 2^21 - 2^19 + 2^15 + 2^9 - 2^7 + 2^4 + 2^2 - 1"
"znprimroot": 23
- "n": 16770049
"n_hex": "0xffe401"
"n_bit": "2^24 - 2^13 + 2^10 + 1"
"n_fac": "2^10 * 3 * 53 * 103 + 1"
"nd": 15721471
"nd_hex": "0xefe3ff"
"nd_bit": "2^24 - 2^20 - 2^13 + 2^10 - 1"
"r2": 1055742
"r2_hex": "0x101bfe"
"r2_bit": "2^20 + 2^13 - 2^10 - 2"
"znprimroot": 11
- "n": 16727041
"n_hex": "0xff3c01"
"n_bit": "2^24 - 2^16 + 2^14 - 2^10 + 1"
"n_fac": "2^10 * 3^3 * 5 * 11^2 + 1"
"nd": 15678463
"nd_hex": "0xef3bff"
"nd_bit": "2^24 - 2^20 - 2^16 + 2^14 - 2^10 - 1"
"r2": 8474475
"r2_hex": "0x814f6b"
"r2_bit": "2^23 + 2^16 + 2^14 + 2^12 - 2^7 - 2^4 - 2^2 - 1"
"znprimroot": 13
- "n": 16665601
"n_hex": "0xfe4c01"
"n_bit": "2^24 - 2^17 + 2^14 + 2^12 - 2^10 + 1"
"n_fac": "2^10 * 3 * 5^2 * 7 * 31 + 1"
"nd": 7228415
"nd_hex": "0x6e4bff"
"nd_bit": "2^23 - 2^20 - 2^17 + 2^14 + 2^12 - 2^10 - 1"
"r2": 8704278
"r2_hex": "0x84d116"
"r2_bit": "2^23 + 2^18 + 2^16 - 2^14 + 2^12 + 2^8 + 2^5 - 2^3 - 2"
"znprimroot": 22
- "n": 16128001
"n_hex": "0xf61801"
"n_bit": "2^24 - 2^19 - 2^17 + 2^13 - 2^11 + 1"
"n_fac": "2^11 * 3^2 * 5^3 * 7 + 1"
"nd": 11933695
"nd_hex": "0xb617ff"
"nd_bit": "2^24 - 2^22 - 2^19 - 2^17 + 2^13 - 2^11 - 1"
"r2": 7066092
"r2_hex": "0x6bd1ec"
"r2_bit": "2^23 - 2^20 - 2^18 - 2^14 + 2^12 + 2^9 - 2^4 - 2^2"
"znprimroot": 13
- "n": 16650241
"n_hex": "0xfe1001"
"n_bit": "2^24 - 2^17 + 2^12 + 1"
"n_fac": "2^12 * 3 * 5 * 271 + 1"
"nd": 16650239
"nd_hex": "0xfe0fff"
"nd_bit": "2^24 - 2^17 + 2^12 - 1"
"r2": 5217337
"r2_hex": "0x4f9c39"
"r2_bit": "2^22 + 2^20 - 2^15 + 2^13 - 2^10 + 2^6 - 2^3 + 1"
"znprimroot": 14
- "n": 15052801
"n_hex": "0xe5b001"
"n_bit": "2^24 - 2^21 + 2^19 - 2^17 - 2^14 - 2^12 + 1"
"n_fac": "2^12 * 3 * 5^2 * 7^2 + 1"
"nd": 15052799
"nd_hex": "0xe5afff"
"nd_bit": "2^24 - 2^21 + 2^19 - 2^17 - 2^14 - 2^12 - 1"
"r2": 1518680
"r2_hex": "0x172c58"
"r2_bit": "2^21 - 2^19 - 2^16 + 2^14 - 2^12 - 2^10 + 2^7 - 2^5 - 2^3"
"znprimroot": 29
- "n": 16736257
"n_hex": "0xff6001"
"n_bit": "2^24 - 2^15 - 2^13 + 1"
"n_fac": "2^13 * 3^2 * 227 + 1"
"nd": 16736255
"nd_hex": "0xff5fff"
"nd_bit": "2^24 - 2^15 - 2^13 - 1"
"r2": 4013981
"r2_hex": "0x3d3f9d"
"r2_bit": "2^22 - 2^18 + 2^16 + 2^14 - 2^7 + 2^5 - 2^2 + 1"
"znprimroot": 5
- "n": 16588801
"n_hex": "0xfd2001"
"n_bit": "2^24 - 2^18 + 2^16 + 2^13 + 1"
"n_fac": "2^13 * 3^4 * 5^2 + 1"
"nd": 16588799
"nd_hex": "0xfd1fff"
"nd_bit": "2^24 - 2^18 + 2^16 + 2^13 - 1"
"r2": 178085
"r2_hex": "0x2b7a5"
"r2_bit": "2^18 - 2^16 - 2^14 - 2^11 - 2^7 + 2^5 + 2^2 + 1"
"znprimroot": 19
- "n": 12902401
"n_hex": "0xc4e001"
"n_bit": "2^24 - 2^22 + 2^18 + 2^16 - 2^13 + 1"
"n_fac": "2^13 * 3^2 * 5^2 * 7 + 1"
"nd": 12902399
"nd_hex": "0xc4dfff"
"nd_bit": "2^24 - 2^22 + 2^18 + 2^16 - 2^13 - 1"
"r2": 2702951
"r2_hex": "0x293e67"
"r2_bit": "2^21 + 2^19 + 2^16 + 2^14 - 2^9 + 2^7 - 2^5 + 2^3 - 1"
"znprimroot": 11
- "n": 16760833
"n_hex": "0xffc001"
"n_bit": "2^24 - 2^14 + 1"
"n_fac": "2^14 * 3 * 11 * 31 + 1"
"nd": 16760831
"nd_hex": "0xffbfff"
"nd_bit": "2^24 - 2^14 - 1"
"r2": 229361
"r2_hex": "0x37ff1"
"r2_bit": "2^18 - 2^15 - 2^4 + 1"
"znprimroot": 7
- "n": 16465921
"n_hex": "0xfb4001"
"n_bit": "2^24 - 2^18 - 2^16 + 2^14 + 1"
"n_fac": "2^14 * 3 * 5 * 67 + 1"
"nd": 16465919
"nd_hex": "0xfb3fff"
"nd_bit": "2^24 - 2^18 - 2^16 + 2^14 - 1"
"r2": 2631940
"r2_hex": "0x282904"
"r2_bit": "2^21 + 2^19 + 2^13 + 2^11 + 2^8 + 2^2"
"znprimroot": 11
- "n": 12042241
"n_hex": "0xb7c001"
"n_bit": "2^24 - 2^22 - 2^19 - 2^14 + 1"
"n_fac": "2^14 * 3 * 5 * 7^2 + 1"
"nd": 12042239
"nd_hex": "0xb7bfff"
"nd_bit": "2^24 - 2^22 - 2^19 - 2^14 - 1"
"r2": 8886127
"r2_hex": "0x87976f"
"r2_bit": "2^23 + 2^19 - 2^15 + 2^13 - 2^11 - 2^7 - 2^4 - 1"
"znprimroot": 19
- "n": 11059201
"n_hex": "0xa8c001"
"n_bit": "2^23 + 2^21 + 2^19 + 2^16 - 2^14 + 1"
"n_fac": "2^14 * 3^3 * 5^2 + 1"
"nd": 11059199
"nd_hex": "0xa8bfff"
"nd_bit": "2^23 + 2^21 + 2^19 + 2^16 - 2^14 - 1"
"r2": 8283001
"r2_hex": "0x7e6379"
"r2_bit": "2^23 - 2^17 + 2^15 - 2^13 + 2^10 - 2^7 - 2^3 + 1"
"znprimroot": 7
- "n": 11304961
"n_hex": "0xac8001"
"n_bit": "2^24 - 2^22 - 2^20 - 2^18 + 2^15 + 1"
"n_fac": "2^15 * 3 * 5 * 23 + 1"
"nd": 11304959
"nd_hex": "0xac7fff"
"nd_bit": "2^24 - 2^22 - 2^20 - 2^18 + 2^15 - 1"
"r2": 10556618
"r2_hex": "0xa114ca"
"r2_bit": "2^23 + 2^21 + 2^16 + 2^12 + 2^10 + 2^8 - 2^6 + 2^3 + 2"
"znprimroot": 7
- "n": 4423681
"n_hex": "0x438001"
"n_bit": "2^22 + 2^18 - 2^15 + 1"
"n_fac": "2^15 * 3^3 * 5 + 1"
"nd": 4423679
"nd_hex": "0x437fff"
"nd_bit": "2^22 + 2^18 - 2^15 - 1"
"r2": 3283126
"r2_hex": "0x3218b6"
"r2_bit": "2^22 - 2^20 + 2^17 + 2^13 - 2^11 + 2^8 - 2^6 - 2^3 - 2"
"znprimroot": 14
- "n": 16580609
"n_hex": "0xfd0001"
"n_bit": "2^24 - 2^18 + 2^16 + 1"
"n_fac": "2^16 * 11 * 23 + 1"
"nd": 16580607
"nd_hex": "0xfcffff"
"nd_bit": "2^24 - 2^18 + 2^16 - 1"
"r2": 4912870
"r2_hex": "0x4af6e6"
"r2_bit": "2^22 + 2^20 - 2^18 - 2^16 - 2^11 - 2^8 - 2^5 + 2^3 - 2"
"znprimroot": 3
- "n": 16515073
"n_hex": "0xfc0001"
"n_bit": "2^24 - 2^18 + 1"
"n_fac": "2^18 * 3^2 * 7 + 1"
"nd": 16515071
"nd_hex": "0xfbffff"
"nd_bit": "2^24 - 2^18 - 1"
"r2": 16248769
"r2_hex": "0xf7efc1"
"r2_bit": "2^24 - 2^19 - 2^12 - 2^6 + 1"
"znprimroot": 5
- "n": 14155777
"n_hex": "0xd80001"
"n_bit": "2^24 - 2^21 - 2^19 + 1"
"n_fac": "2^19 * 3^3 + 1"
"nd": 14155775
"nd_hex": "0xd7ffff"
"nd_bit": "2^24 - 2^21 - 2^19 - 1"
"r2": 6330294
"r2_hex": "0x6097b6"
"r2_bit": "2^23 - 2^21 + 2^15 + 2^13 - 2^11 - 2^6 - 2^3 - 2"
"znprimroot": 7
- "n": 13631489
"n_hex": "0xd00001"
"n_bit": "2^24 - 2^22 + 2^20 + 1"
"n_fac": "2^20 * 13 + 1"
"nd": 13631487
"nd_hex": "0xcfffff"
"nd_bit": "2^24 - 2^22 + 2^20 - 1"
"r2": 9759825
"r2_hex": "0x94ec51"
"r2_bit": "2^23 + 2^20 + 2^18 + 2^16 - 2^12 - 2^10 + 2^6 + 2^4 + 1"
"znprimroot": 15
Raw
result_prime_0025.yaml
- "r": 25
"primes":
- "n": 33554383
"n_hex": "0x1ffffcf"
"n_bit": "2^25 - 2^6 + 2^4 - 1"
"n_fac": "2 * 3 * 1367 * 4091 + 1"
"nd": 2054353
"nd_hex": "0x1f58d1"
"nd_bit": "2^21 - 2^15 - 2^13 - 2^11 + 2^8 - 2^6 + 2^4 + 1"
"r2": 2401
"r2_hex": "0x961"
"r2_bit": "2^11 + 2^9 - 2^7 - 2^5 + 1"
"znprimroot": 3
- "n": 33554371
"n_hex": "0x1ffffc3"
"n_bit": "2^25 - 2^6 + 2^2 - 1"
"n_fac": "2 * 3 * 5 * 1118479 + 1"
"nd": 17602325
"nd_hex": "0x10c9715"
"nd_bit": "2^24 + 2^20 - 2^18 + 2^15 + 2^13 - 2^11 - 2^8 + 2^4 + 2^2 + 1"
"r2": 3721
"r2_hex": "0xe89"
"r2_bit": "2^12 - 2^9 + 2^7 + 2^3 + 1"
"znprimroot": 2
- "n": 33553171
"n_hex": "0x1fffb13"
"n_bit": "2^25 - 2^10 - 2^8 + 2^4 + 2^2 - 1"
"n_fac": "2 * 3^3 * 5 * 7 * 41 * 433 + 1"
"nd": 21952741
"nd_hex": "0x14ef8e5"
"nd_bit": "2^24 + 2^22 + 2^20 - 2^16 - 2^11 + 2^8 - 2^5 + 2^2 + 1"
"r2": 1590121
"r2_hex": "0x184369"
"r2_bit": "2^21 - 2^19 + 2^14 + 2^10 - 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 7
- "n": 33554341
"n_hex": "0x1ffffa5"
"n_bit": "2^25 - 2^7 + 2^5 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5 * 131 * 1423 + 1"
"nd": 16592851
"nd_hex": "0xfd2fd3"
"nd_bit": "2^24 - 2^18 + 2^16 + 2^14 - 2^12 - 2^6 + 2^4 + 2^2 - 1"
"r2": 8281
"r2_hex": "0x2059"
"r2_bit": "2^13 + 2^7 - 2^5 - 2^3 + 1"
"znprimroot": 6
- "n": 33554221
"n_hex": "0x1ffff2d"
"n_bit": "2^25 - 2^8 + 2^6 - 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 7^2 * 101 * 113 + 1"
"nd": 6838107
"nd_hex": "0x68575b"
"nd_bit": "2^23 - 2^21 + 2^19 + 2^15 - 2^13 - 2^11 - 2^7 - 2^5 - 2^2 - 1"
"r2": 44521
"r2_hex": "0xade9"
"r2_bit": "2^16 - 2^14 - 2^12 - 2^9 - 2^5 + 2^3 + 1"
"znprimroot": 2
- "n": 33550021
"n_hex": "0x1ffeec5"
"n_bit": "2^25 - 2^12 - 2^8 - 2^6 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5 * 7 * 26627 + 1"
"nd": 32808947
"nd_hex": "0x1f49ff3"
"nd_bit": "2^25 - 2^20 + 2^18 + 2^15 + 2^13 - 2^4 + 2^2 - 1"
"r2": 19456921
"r2_hex": "0x128e399"
"r2_bit": "2^24 + 2^21 + 2^19 + 2^16 - 2^13 + 2^10 - 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 33554393
"n_hex": "0x1ffffd9"
"n_bit": "2^25 - 2^5 - 2^3 + 1"
"n_fac": "2^3 * 29 * 61 * 2371 + 1"
"nd": 16347031
"nd_hex": "0xf96f97"
"nd_bit": "2^24 - 2^19 + 2^17 - 2^15 - 2^12 - 2^7 + 2^5 - 2^3 - 1"
"r2": 1521
"r2_hex": "0x5f1"
"r2_bit": "2^11 - 2^9 - 2^4 + 1"
"znprimroot": 3
- "n": 33554137
"n_hex": "0x1fffed9"
"n_bit": "2^25 - 2^8 - 2^5 - 2^3 + 1"
"n_fac": "2^3 * 3 * 7 * 11 * 67 * 271 + 1"
"nd": 28663447
"nd_hex": "0x1b55e97"
"nd_bit": "2^25 - 2^22 - 2^19 - 2^17 - 2^15 - 2^13 - 2^9 + 2^7 + 2^5 - 2^3 - 1"
"r2": 87025
"r2_hex": "0x153f1"
"r2_bit": "2^16 + 2^14 + 2^12 + 2^10 - 2^4 + 1"
"znprimroot": 15
- "n": 33553657
"n_hex": "0x1fffcf9"
"n_bit": "2^25 - 2^10 + 2^8 - 2^3 + 1"
"n_fac": "2^3 * 3^3 * 31 * 5011 + 1"
"nd": 24115895
"nd_hex": "0x16ffab7"
"nd_bit": "2^25 - 2^23 - 2^20 - 2^10 - 2^8 - 2^6 - 2^3 - 1"
"r2": 600625
"r2_hex": "0x92a31"
"r2_bit": "2^19 + 2^16 + 2^13 + 2^11 + 2^9 + 2^6 - 2^4 + 1"
"znprimroot": 10
- "n": 33550441
"n_hex": "0x1fff069"
"n_bit": "2^25 - 2^12 + 2^7 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 7 * 11 * 3631 + 1"
"nd": 27484199
"nd_hex": "0x1a36027"
"nd_bit": "2^25 - 2^23 + 2^21 + 2^18 - 2^15 - 2^13 + 2^5 + 2^3 - 1"
"r2": 15928081
"r2_hex": "0xf30b11"
"r2_bit": "2^24 - 2^20 + 2^18 - 2^16 + 2^12 - 2^10 - 2^8 + 2^4 + 1"
"znprimroot": 19
- "n": 33553969
"n_hex": "0x1fffe31"
"n_bit": "2^25 - 2^9 + 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3 * 7 * 37 * 2699 + 1"
"nd": 23553327
"nd_hex": "0x167652f"
"nd_bit": "2^25 - 2^23 - 2^21 + 2^19 - 2^15 - 2^13 + 2^10 + 2^8 + 2^6 - 2^4 - 1"
"r2": 214369
"r2_hex": "0x34561"
"r2_bit": "2^18 - 2^16 + 2^14 + 2^11 - 2^9 - 2^7 - 2^5 + 1"
"znprimroot": 29
- "n": 33552721
"n_hex": "0x1fff951"
"n_bit": "2^25 - 2^11 + 2^8 + 2^6 + 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5 * 46601 + 1"
"nd": 6099023
"nd_hex": "0x5d104f"
"nd_bit": "2^23 - 2^21 - 2^18 + 2^16 + 2^12 + 2^6 + 2^4 - 1"
"r2": 2927521
"r2_hex": "0x2caba1"
"r2_bit": "2^22 - 2^20 - 2^18 + 2^16 - 2^14 - 2^12 - 2^10 - 2^7 + 2^5 + 1"
"znprimroot": 7
- "n": 33541201
"n_hex": "0x1ffcc51"
"n_bit": "2^25 - 2^14 + 2^12 - 2^10 + 2^6 + 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5^2 * 7 * 11^3 + 1"
"nd": 3867471
"nd_hex": "0x3b034f"
"nd_bit": "2^22 - 2^18 - 2^16 + 2^10 - 2^8 + 2^6 + 2^4 - 1"
"r2": 7353356
"r2_hex": "0x70340c"
"r2_bit": "2^23 - 2^20 + 2^14 - 2^12 + 2^10 + 2^4 - 2^2"
"znprimroot": 13
- "n": 33554273
"n_hex": "0x1ffff61"
"n_bit": "2^25 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 1048571 + 1"
"nd": 11606879
"nd_hex": "0xb11b5f"
"nd_bit": "2^24 - 2^22 - 2^20 + 2^16 + 2^13 - 2^10 - 2^7 - 2^5 - 1"
"r2": 25281
"r2_hex": "0x62c1"
"r2_bit": "2^15 - 2^13 + 2^10 - 2^8 - 2^6 + 1"
"znprimroot": 3
- "n": 33553633
"n_hex": "0x1fffce1"
"n_bit": "2^25 - 2^10 + 2^8 - 2^5 + 1"
"n_fac": "2^5 * 3 * 7^3 * 1019 + 1"
"nd": 23181535
"nd_hex": "0x161b8df"
"nd_bit": "2^25 - 2^23 - 2^21 + 2^17 - 2^14 - 2^11 + 2^8 - 2^5 - 1"
"r2": 638401
"r2_hex": "0x9bdc1"
"r2_bit": "2^19 + 2^17 - 2^14 - 2^9 - 2^6 + 1"
"znprimroot": 15
- "n": 33552481
"n_hex": "0x1fff861"
"n_bit": "2^25 - 2^11 + 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 13 * 19 * 283 + 1"
"nd": 23286879
"nd_hex": "0x163545f"
"nd_bit": "2^25 - 2^23 - 2^21 + 2^18 - 2^16 + 2^14 + 2^12 + 2^10 + 2^7 - 2^5 - 1"
"r2": 3806401
"r2_hex": "0x3a14c1"
"r2_bit": "2^22 - 2^19 + 2^17 + 2^12 + 2^10 + 2^8 - 2^6 + 1"
"znprimroot": 11
- "n": 33549601
"n_hex": "0x1ffed21"
"n_bit": "2^25 - 2^12 - 2^10 + 2^8 + 2^5 + 1"
"n_fac": "2^5 * 3 * 5^2 * 7 * 1997 + 1"
"nd": 534815
"nd_hex": "0x8291f"
"nd_bit": "2^19 + 2^13 + 2^11 + 2^8 + 2^5 - 1"
"r2": 23338561
"r2_hex": "0x1641e41"
"r2_bit": "2^25 - 2^23 - 2^21 + 2^18 + 2^13 - 2^9 + 2^6 + 1"
"znprimroot": 13
- "n": 33536161
"n_hex": "0x1ffb8a1"
"n_bit": "2^25 - 2^14 - 2^11 + 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5 * 7 * 1109 + 1"
"nd": 15193247
"nd_hex": "0xe7d49f"
"nd_bit": "2^24 - 2^21 + 2^19 - 2^14 + 2^12 + 2^10 + 2^7 + 2^5 - 1"
"r2": 32003992
"r2_hex": "0x1e85798"
"r2_bit": "2^25 - 2^21 + 2^19 + 2^15 - 2^13 - 2^11 - 2^7 + 2^5 - 2^3"
"znprimroot": 19
- "n": 33551041
"n_hex": "0x1fff2c1"
"n_bit": "2^25 - 2^12 + 2^10 - 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 34949 + 1"
"nd": 1860287
"nd_hex": "0x1c62bf"
"nd_bit": "2^21 - 2^18 + 2^15 - 2^13 + 2^10 - 2^8 - 2^6 - 1"
"r2": 11498881
"r2_hex": "0xaf7581"
"r2_bit": "2^24 - 2^22 - 2^20 - 2^15 - 2^11 - 2^9 - 2^7 + 1"
"znprimroot": 7
- "n": 33364801
"n_hex": "0x1fd1b41"
"n_bit": "2^25 - 2^18 + 2^16 + 2^13 - 2^10 - 2^8 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5^2 * 7 * 331 + 1"
"nd": 6982463
"nd_hex": "0x6a8b3f"
"nd_bit": "2^23 - 2^21 + 2^19 + 2^17 + 2^15 + 2^12 - 2^10 - 2^8 + 2^6 - 1"
"r2": 26025484
"r2_hex": "0x18d1e0c"
"r2_bit": "2^25 - 2^23 + 2^20 - 2^18 + 2^16 + 2^13 - 2^9 + 2^4 - 2^2"
"znprimroot": 19
- "n": 33553537
"n_hex": "0x1fffc81"
"n_bit": "2^25 - 2^10 + 2^7 + 1"
"n_fac": "2^7 * 3 * 59 * 1481 + 1"
"nd": 18070655
"nd_hex": "0x113bc7f"
"nd_bit": "2^24 + 2^20 + 2^18 - 2^14 - 2^10 + 2^7 - 1"
"r2": 801025
"r2_hex": "0xc3901"
"r2_bit": "2^20 - 2^18 + 2^14 - 2^11 + 2^8 + 1"
"znprimroot": 7
- "n": 33532801
"n_hex": "0x1ffab81"
"n_bit": "2^25 - 2^14 - 2^12 - 2^10 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5^2 * 7 * 499 + 1"
"nd": 16477055
"nd_hex": "0xfb6b7f"
"nd_bit": "2^24 - 2^18 - 2^15 - 2^12 - 2^10 - 2^7 - 1"
"r2": 31973748
"r2_hex": "0x1e7e174"
"r2_bit": "2^25 - 2^21 + 2^19 - 2^13 + 2^9 - 2^7 - 2^4 + 2^2"
"znprimroot": 17
- "n": 33528961
"n_hex": "0x1ff9c81"
"n_bit": "2^25 - 2^15 + 2^13 - 2^10 + 2^7 + 1"
"n_fac": "2^7 * 3^2 * 5 * 5821 + 1"
"nd": 7560319
"nd_hex": "0x735c7f"
"nd_bit": "2^23 - 2^20 + 2^18 - 2^15 - 2^13 - 2^10 + 2^7 - 1"
"r2": 11721582
"r2_hex": "0xb2db6e"
"r2_bit": "2^24 - 2^22 - 2^20 + 2^18 - 2^16 - 2^13 - 2^10 - 2^7 - 2^4 - 2"
"znprimroot": 13
- "n": 33264001
"n_hex": "0x1fb9181"
"n_bit": "2^25 - 2^18 - 2^15 + 2^12 + 2^9 - 2^7 + 1"
"n_fac": "2^7 * 3^3 * 5^3 * 7 * 11 + 1"
"nd": 27873663
"nd_hex": "0x1a9517f"
"nd_bit": "2^25 - 2^23 + 2^21 + 2^19 + 2^16 + 2^14 + 2^12 + 2^9 - 2^7 - 1"
"r2": 25923226
"r2_hex": "0x18b8e9a"
"r2_bit": "2^25 - 2^23 + 2^20 - 2^18 - 2^15 + 2^12 - 2^9 + 2^7 + 2^5 - 2^3 + 2"
"znprimroot": 46
- "n": 33553153
"n_hex": "0x1fffb01"
"n_bit": "2^25 - 2^10 - 2^8 + 1"
"n_fac": "2^8 * 3^2 * 14563 + 1"
"nd": 15137535
"nd_hex": "0xe6faff"
"nd_bit": "2^24 - 2^21 + 2^19 - 2^16 - 2^10 - 2^8 - 1"
"r2": 1635841
"r2_hex": "0x18f601"
"r2_bit": "2^21 - 2^19 + 2^16 - 2^11 - 2^9 + 1"
"znprimroot": 5
- "n": 33550081
"n_hex": "0x1ffef01"
"n_bit": "2^25 - 2^12 - 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 8737 + 1"
"nd": 31387391
"nd_hex": "0x1deeeff"
"nd_bit": "2^25 - 2^21 - 2^16 - 2^12 - 2^8 - 1"
"r2": 18931201
"r2_hex": "0x120de01"
"r2_bit": "2^24 + 2^21 + 2^16 - 2^13 - 2^9 + 1"
"znprimroot": 17
- "n": 33411841
"n_hex": "0x1fdd301"
"n_bit": "2^25 - 2^17 - 2^14 + 2^12 + 2^10 - 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 7 * 11 * 113 + 1"
"nd": 18141951
"nd_hex": "0x114d2ff"
"nd_bit": "2^24 + 2^20 + 2^18 + 2^16 - 2^14 + 2^12 + 2^10 - 2^8 - 1"
"r2": 17793953
"r2_hex": "0x10f83a1"
"r2_bit": "2^24 + 2^20 - 2^15 + 2^10 - 2^7 + 2^5 + 1"
"znprimroot": 17
- "n": 33396481
"n_hex": "0x1fd9701"
"n_bit": "2^25 - 2^17 - 2^15 + 2^13 - 2^11 - 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5 * 13 * 223 + 1"
"nd": 32282367
"nd_hex": "0x1ec96ff"
"nd_bit": "2^25 - 2^20 - 2^18 + 2^15 + 2^13 - 2^11 - 2^8 - 1"
"r2": 1347094
"r2_hex": "0x148e16"
"r2_bit": "2^20 + 2^18 + 2^15 + 2^12 - 2^9 + 2^5 - 2^3 - 2"
"znprimroot": 11
- "n": 33551873
"n_hex": "0x1fff601"
"n_bit": "2^25 - 2^11 - 2^9 + 1"
"n_fac": "2^9 * 19 * 3449 + 1"
"nd": 26998271
"nd_hex": "0x19bf5ff"
"nd_bit": "2^25 - 2^23 + 2^21 - 2^18 - 2^11 - 2^9 - 1"
"r2": 6548481
"r2_hex": "0x63ec01"
"r2_bit": "2^23 - 2^21 + 2^18 - 2^12 - 2^10 + 1"
"znprimroot": 5
- "n": 33550849
"n_hex": "0x1fff201"
"n_bit": "2^25 - 2^12 + 2^9 + 1"
"n_fac": "2^9 * 3^4 * 809 + 1"
"nd": 20705791
"nd_hex": "0x13bf1ff"
"nd_bit": "2^24 + 2^22 - 2^18 - 2^12 + 2^9 - 1"
"r2": 12837889
"r2_hex": "0xc3e401"
"r2_bit": "2^24 - 2^22 + 2^18 - 2^13 + 2^10 + 1"
"znprimroot": 13
- "n": 33292801
"n_hex": "0x1fc0201"
"n_bit": "2^25 - 2^18 + 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5^2 * 17^2 + 1"
"nd": 33030655
"nd_hex": "0x1f801ff"
"nd_bit": "2^25 - 2^19 + 2^9 - 1"
"r2": 781305
"r2_hex": "0xbebf9"
"r2_bit": "2^20 - 2^18 - 2^12 - 2^10 - 2^3 + 1"
"znprimroot": 7
- "n": 33481729
"n_hex": "0x1fee401"
"n_bit": "2^25 - 2^16 - 2^13 + 2^10 + 1"
"n_fac": "2^10 * 3^3 * 7 * 173 + 1"
"nd": 15655935
"nd_hex": "0xeee3ff"
"nd_bit": "2^24 - 2^20 - 2^16 - 2^13 + 2^10 - 1"
"r2": 29094756
"r2_hex": "0x1bbf364"
"r2_bit": "2^25 - 2^22 - 2^18 - 2^12 + 2^10 - 2^7 - 2^5 + 2^2"
"znprimroot": 11
- "n": 33469441
"n_hex": "0x1feb401"
"n_bit": "2^25 - 2^16 - 2^14 - 2^12 + 2^10 + 1"
"n_fac": "2^10 * 3 * 5 * 2179 + 1"
"nd": 24032255
"nd_hex": "0x16eb3ff"
"nd_bit": "2^25 - 2^23 - 2^20 - 2^16 - 2^14 - 2^12 + 2^10 - 1"
"r2": 27540266
"r2_hex": "0x1a43b2a"
"r2_bit": "2^25 - 2^23 + 2^21 + 2^18 + 2^14 - 2^10 - 2^8 + 2^5 + 2^3 + 2"
"znprimroot": 13
- "n": 33223681
"n_hex": "0x1faf401"
"n_bit": "2^25 - 2^18 - 2^16 - 2^12 + 2^10 + 1"
"n_fac": "2^10 * 3^2 * 5 * 7 * 103 + 1"
"nd": 23786495
"nd_hex": "0x16af3ff"
"nd_bit": "2^25 - 2^23 - 2^20 - 2^18 - 2^16 - 2^12 + 2^10 - 1"
"r2": 23866149
"r2_hex": "0x16c2b25"
"r2_bit": "2^25 - 2^23 - 2^20 - 2^18 + 2^14 - 2^12 - 2^10 - 2^8 + 2^5 + 2^2 + 1"
"znprimroot": 11
- "n": 33540097
"n_hex": "0x1ffc801"
"n_bit": "2^25 - 2^14 + 2^11 + 1"
"n_fac": "2^11 * 3 * 53 * 103 + 1"
"nd": 29345791
"nd_hex": "0x1bfc7ff"
"nd_bit": "2^25 - 2^22 - 2^14 + 2^11 - 1"
"r2": 4251643
"r2_hex": "0x40dffb"
"r2_bit": "2^22 + 2^16 - 2^13 - 2^2 - 1"
"znprimroot": 5
- "n": 33380353
"n_hex": "0x1fd5801"
"n_bit": "2^25 - 2^17 - 2^15 - 2^13 - 2^11 + 1"
"n_fac": "2^11 * 3^2 * 1811 + 1"
"nd": 29186047
"nd_hex": "0x1bd57ff"
"nd_bit": "2^25 - 2^22 - 2^17 - 2^15 - 2^13 - 2^11 - 1"
"r2": 27518070
"r2_hex": "0x1a3e476"
"r2_bit": "2^25 - 2^23 + 2^21 + 2^18 - 2^13 + 2^10 + 2^7 - 2^3 - 2"
"znprimroot": 5
- "n": 33331201
"n_hex": "0x1fc9801"
"n_bit": "2^25 - 2^18 + 2^15 + 2^13 - 2^11 + 1"
"n_fac": "2^11 * 3 * 5^2 * 7 * 31 + 1"
"nd": 29136895
"nd_hex": "0x1bc97ff"
"nd_bit": "2^25 - 2^22 - 2^18 + 2^15 + 2^13 - 2^11 - 1"
"r2": 1933866
"r2_hex": "0x1d822a"
"r2_bit": "2^21 - 2^17 - 2^15 + 2^9 + 2^5 + 2^3 + 2"
"znprimroot": 22
- "n": 33550337
"n_hex": "0x1fff001"
"n_bit": "2^25 - 2^12 + 1"
"n_fac": "2^12 * 8191 + 1"
"nd": 16773119
"nd_hex": "0xffefff"
"nd_bit": "2^24 - 2^12 - 1"
"r2": 16769025
"r2_hex": "0xffe001"
"r2_bit": "2^24 - 2^13 + 1"
"znprimroot": 3
- "n": 33533953
"n_hex": "0x1ffb001"
"n_bit": "2^25 - 2^14 - 2^12 + 1"
"n_fac": "2^12 * 3 * 2729 + 1"
"nd": 16756735
"nd_hex": "0xffafff"
"nd_bit": "2^24 - 2^14 - 2^12 - 1"
"r2": 16982005
"r2_hex": "0x1031ff5"
"r2_bit": "2^24 + 2^18 - 2^16 + 2^13 - 2^4 + 2^2 + 1"
"znprimroot": 5
- "n": 32256001
"n_hex": "0x1ec3001"
"n_bit": "2^25 - 2^20 - 2^18 + 2^14 - 2^12 + 1"
"n_fac": "2^12 * 3^2 * 5^3 * 7 + 1"
"nd": 15478783
"nd_hex": "0xec2fff"
"nd_bit": "2^24 - 2^20 - 2^18 + 2^14 - 2^12 - 1"
"r2": 30913495
"r2_hex": "0x1d7b3d7"
"r2_bit": "2^25 - 2^21 - 2^19 - 2^14 - 2^12 + 2^10 - 2^5 - 2^3 - 1"
"znprimroot": 11
- "n": 33349633
"n_hex": "0x1fce001"
"n_bit": "2^25 - 2^18 + 2^16 - 2^13 + 1"
"n_fac": "2^13 * 3 * 23 * 59 + 1"
"nd": 33349631
"nd_hex": "0x1fcdfff"
"nd_bit": "2^25 - 2^18 + 2^16 - 2^13 - 1"
"r2": 22141720
"r2_hex": "0x151db18"
"r2_bit": "2^24 + 2^22 + 2^20 + 2^17 - 2^13 - 2^10 - 2^8 + 2^5 - 2^3"
"znprimroot": 5
- "n": 33538049
"n_hex": "0x1ffc001"
"n_bit": "2^25 - 2^14 + 1"
"n_fac": "2^14 * 23 * 89 + 1"
"nd": 33538047
"nd_hex": "0x1ffbfff"
"nd_bit": "2^25 - 2^14 - 1"
"r2": 98297
"r2_hex": "0x17ff9"
"r2_bit": "2^17 - 2^15 - 2^3 + 1"
"znprimroot": 3
- "n": 33177601
"n_hex": "0x1fa4001"
"n_bit": "2^25 - 2^19 + 2^17 + 2^14 + 1"
"n_fac": "2^14 * 3^4 * 5^2 + 1"
"nd": 33177599
"nd_hex": "0x1fa3fff"
"nd_bit": "2^25 - 2^19 + 2^17 + 2^14 - 1"
"r2": 1470281
"r2_hex": "0x166f49"
"r2_bit": "2^21 - 2^19 - 2^17 + 2^15 - 2^12 - 2^8 + 2^6 + 2^3 + 1"
"znprimroot": 26
- "n": 32686081
"n_hex": "0x1f2c001"
"n_bit": "2^25 - 2^20 + 2^18 - 2^16 - 2^14 + 1"
"n_fac": "2^14 * 3 * 5 * 7 * 19 + 1"
"nd": 32686079
"nd_hex": "0x1f2bfff"
"nd_bit": "2^25 - 2^20 + 2^18 - 2^16 - 2^14 - 1"
"r2": 30942693
"r2_hex": "0x1d825e5"
"r2_bit": "2^25 - 2^21 - 2^19 + 2^13 + 2^11 - 2^9 - 2^5 + 2^2 + 1"
"znprimroot": 22
- "n": 33128449
"n_hex": "0x1f98001"
"n_bit": "2^25 - 2^19 + 2^17 - 2^15 + 1"
"n_fac": "2^15 * 3 * 337 + 1"
"nd": 33128447
"nd_hex": "0x1f97fff"
"nd_bit": "2^25 - 2^19 + 2^17 - 2^15 - 1"
"r2": 17001116
"r2_hex": "0x1036a9c"
"r2_bit": "2^24 + 2^18 - 2^15 - 2^13 + 2^11 + 2^9 + 2^7 + 2^5 - 2^2"
"znprimroot": 11
- "n": 32931841
"n_hex": "0x1f68001"
"n_bit": "2^25 - 2^19 - 2^17 + 2^15 + 1"
"n_fac": "2^15 * 3 * 5 * 67 + 1"
"nd": 32931839
"nd_hex": "0x1f67fff"
"nd_bit": "2^25 - 2^19 - 2^17 + 2^15 - 1"
"r2": 11784711
"r2_hex": "0xb3d207"
"r2_bit": "2^24 - 2^22 - 2^20 + 2^18 - 2^14 + 2^12 + 2^9 + 2^3 - 1"
"znprimroot": 14
- "n": 30965761
"n_hex": "0x1d88001"
"n_bit": "2^25 - 2^21 - 2^19 + 2^15 + 1"
"n_fac": "2^15 * 3^3 * 5 * 7 + 1"
"nd": 30965759
"nd_hex": "0x1d87fff"
"nd_bit": "2^25 - 2^21 - 2^19 + 2^15 - 1"
"r2": 10105514
"r2_hex": "0x9a32aa"
"r2_bit": "2^23 + 2^21 - 2^19 + 2^17 + 2^14 - 2^12 + 2^9 + 2^7 + 2^5 + 2^3 + 2"
"znprimroot": 39
- "n": 32440321
"n_hex": "0x1ef0001"
"n_bit": "2^25 - 2^20 - 2^16 + 1"
"n_fac": "2^16 * 3^2 * 5 * 11 + 1"
"nd": 32440319
"nd_hex": "0x1eeffff"
"nd_bit": "2^25 - 2^20 - 2^16 - 1"
"r2": 11758219
"r2_hex": "0xb36a8b"
"r2_bit": "2^24 - 2^22 - 2^20 + 2^18 - 2^15 - 2^13 + 2^11 + 2^9 + 2^7 + 2^4 - 2^2 - 1"
"znprimroot": 41
- "n": 21626881
"n_hex": "0x14a0001"
"n_bit": "2^24 + 2^22 + 2^19 + 2^17 + 1"
"n_fac": "2^17 * 3 * 5 * 11 + 1"
"nd": 21626879
"nd_hex": "0x149ffff"
"nd_bit": "2^24 + 2^22 + 2^19 + 2^17 - 1"
"r2": 5218257
"r2_hex": "0x4f9fd1"
"r2_bit": "2^22 + 2^20 - 2^15 + 2^13 - 2^6 + 2^4 + 1"
"znprimroot": 14
- "n": 33292289
"n_hex": "0x1fc0001"
"n_bit": "2^25 - 2^18 + 1"
"n_fac": "2^18 * 127 + 1"
"nd": 33292287
"nd_hex": "0x1fbffff"
"nd_bit": "2^25 - 2^18 - 1"
"r2": 3667953
"r2_hex": "0x37f7f1"
"r2_bit": "2^22 - 2^19 - 2^11 - 2^4 + 1"
"znprimroot": 3
- "n": 29884417
"n_hex": "0x1c80001"
"n_bit": "2^25 - 2^22 + 2^19 + 1"
"n_fac": "2^19 * 3 * 19 + 1"
"nd": 29884415
"nd_hex": "0x1c7ffff"
"nd_bit": "2^25 - 2^22 + 2^19 - 1"
"r2": 13705074
"r2_hex": "0xd11f72"
"r2_bit": "2^24 - 2^22 + 2^20 + 2^16 + 2^13 - 2^7 - 2^4 + 2"
"znprimroot": 5
- "n": 28311553
"n_hex": "0x1b00001"
"n_bit": "2^25 - 2^22 - 2^20 + 1"
"n_fac": "2^20 * 3^3 + 1"
"nd": 28311551
"nd_hex": "0x1afffff"
"nd_bit": "2^25 - 2^22 - 2^20 - 1"
"r2": 8466282
"r2_hex": "0x812f6a"
"r2_bit": "2^23 + 2^16 + 2^14 - 2^12 - 2^7 - 2^5 + 2^3 + 2"
"znprimroot": 5
- "n": 23068673
"n_hex": "0x1600001"
"n_bit": "2^25 - 2^23 - 2^21 + 1"
"n_fac": "2^21 * 11 + 1"
"nd": 23068671
"nd_hex": "0x15fffff"
"nd_bit": "2^25 - 2^23 - 2^21 - 1"
"r2": 9913812
"r2_hex": "0x9745d4"
"r2_bit": "2^23 + 2^21 - 2^19 - 2^16 + 2^14 + 2^11 - 2^9 - 2^6 + 2^4 + 2^2"
"znprimroot": 3
Raw
result_prime_0026.yaml
- "r": 26
"primes":
- "n": 67108859
"n_hex": "0x3fffffb"
"n_bit": "2^26 - 2^2 - 1"
"n_fac": "2 * 479 * 70051 + 1"
"nd": 13421773
"nd_hex": "0xcccccd"
"nd_bit": "2^24 - 2^22 + 2^20 - 2^18 + 2^16 - 2^14 + 2^12 - 2^10 + 2^8 - 2^6 + 2^4 - 2^2 + 1"
"r2": 25
"r2_hex": "0x19"
"r2_bit": "2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 67108471
"n_hex": "0x3fffe77"
"n_bit": "2^26 - 2^9 + 2^7 - 2^3 - 1"
"n_fac": "2 * 3 * 5 * 11 * 13 * 15643 + 1"
"nd": 29541561
"nd_hex": "0x1c2c4b9"
"nd_bit": "2^25 - 2^22 + 2^18 - 2^16 - 2^14 + 2^10 + 2^8 - 2^6 - 2^3 + 1"
"r2": 154449
"r2_hex": "0x25b51"
"r2_bit": "2^17 + 2^15 - 2^13 - 2^10 - 2^8 + 2^6 + 2^4 + 1"
"znprimroot": 3
- "n": 67107871
"n_hex": "0x3fffc1f"
"n_bit": "2^26 - 2^10 + 2^5 - 1"
"n_fac": "2 * 3^2 * 5 * 31 * 67 * 359 + 1"
"nd": 66027553
"nd_hex": "0x3ef8021"
"nd_bit": "2^26 - 2^20 - 2^15 + 2^5 + 1"
"r2": 986049
"r2_hex": "0xf0bc1"
"r2_bit": "2^20 - 2^16 + 2^12 - 2^10 - 2^6 + 1"
"znprimroot": 3
- "n": 67105711
"n_hex": "0x3fff3af"
"n_bit": "2^26 - 2^12 + 2^10 - 2^6 - 2^4 - 1"
"n_fac": "2 * 3^2 * 5 * 7 * 29 * 3673 + 1"
"nd": 19709105
"nd_hex": "0x12cbcb1"
"nd_bit": "2^24 + 2^22 - 2^20 - 2^18 + 2^16 - 2^14 - 2^10 + 2^8 - 2^6 - 2^4 + 1"
"r2": 9941409
"r2_hex": "0x97b1a1"
"r2_bit": "2^23 + 2^21 - 2^19 - 2^14 - 2^12 + 2^9 - 2^7 + 2^5 + 1"
"znprimroot": 3
- "n": 67108837
"n_hex": "0x3ffffe5"
"n_bit": "2^26 - 2^5 + 2^2 + 1"
"n_fac": "2^2 * 3 * 19 * 294337 + 1"
"nd": 4971027
"nd_hex": "0x4bda13"
"nd_bit": "2^22 + 2^20 - 2^18 - 2^13 - 2^11 + 2^9 + 2^4 + 2^2 - 1"
"r2": 729
"r2_hex": "0x2d9"
"r2_bit": "2^10 - 2^8 - 2^5 - 2^3 + 1"
"znprimroot": 5
- "n": 67108777
"n_hex": "0x3ffffa9"
"n_bit": "2^26 - 2^7 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 7 * 173 * 2309 + 1"
"nd": 64023399
"nd_hex": "0x3d0eb67"
"nd_bit": "2^26 - 2^22 + 2^20 + 2^16 - 2^12 - 2^10 - 2^7 - 2^5 + 2^3 - 1"
"r2": 7569
"r2_hex": "0x1d91"
"r2_bit": "2^13 - 2^9 - 2^7 + 2^4 + 1"
"znprimroot": 5
- "n": 67108201
"n_hex": "0x3fffd69"
"n_bit": "2^26 - 2^9 - 2^7 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5^2 * 111847 + 1"
"nd": 50306343
"nd_hex": "0x2ff9d27"
"nd_bit": "2^26 - 2^24 - 2^15 + 2^13 - 2^10 + 2^8 + 2^5 + 2^3 - 1"
"r2": 439569
"r2_hex": "0x6b511"
"r2_bit": "2^19 - 2^16 - 2^14 - 2^12 + 2^10 + 2^8 + 2^4 + 1"
"znprimroot": 7
- "n": 67107241
"n_hex": "0x3fff9a9"
"n_bit": "2^26 - 2^11 + 2^9 - 2^7 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5 * 19 * 9811 + 1"
"nd": 49825127
"nd_hex": "0x2f84567"
"nd_bit": "2^26 - 2^24 - 2^19 + 2^14 + 2^11 - 2^9 - 2^7 - 2^5 + 2^3 - 1"
"r2": 2634129
"r2_hex": "0x283191"
"r2_bit": "2^21 + 2^19 + 2^14 - 2^12 + 2^9 - 2^7 + 2^4 + 1"
"znprimroot": 13
- "n": 67106761
"n_hex": "0x3fff7c9"
"n_bit": "2^26 - 2^11 - 2^6 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 7 * 79889 + 1"
"nd": 12987783
"nd_hex": "0xc62d87"
"nd_bit": "2^24 - 2^22 + 2^19 - 2^17 + 2^14 - 2^12 - 2^9 - 2^7 + 2^3 - 1"
"r2": 4422609
"r2_hex": "0x437bd1"
"r2_bit": "2^22 + 2^18 - 2^15 - 2^10 - 2^6 + 2^4 + 1"
"znprimroot": 11
- "n": 67105081
"n_hex": "0x3fff139"
"n_bit": "2^26 - 2^12 + 2^8 + 2^6 - 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5 * 7 * 31 * 859 + 1"
"nd": 18502391
"nd_hex": "0x11a52f7"
"nd_bit": "2^24 + 2^21 - 2^19 + 2^17 + 2^14 + 2^12 + 2^10 - 2^8 - 2^3 - 1"
"r2": 14311089
"r2_hex": "0xda5eb1"
"r2_bit": "2^24 - 2^21 - 2^19 + 2^17 + 2^15 - 2^13 - 2^8 - 2^6 - 2^4 + 1"
"znprimroot": 33
- "n": 67108753
"n_hex": "0x3ffff91"
"n_bit": "2^26 - 2^7 + 2^4 + 1"
"n_fac": "2^4 * 3^2 * 466033 + 1"
"nd": 51994255
"nd_hex": "0x3195e8f"
"nd_bit": "2^26 - 2^24 + 2^21 - 2^19 + 2^17 - 2^15 - 2^13 - 2^9 + 2^7 + 2^4 - 1"
"r2": 12321
"r2_hex": "0x3021"
"r2_bit": "2^14 - 2^12 + 2^5 + 1"
"znprimroot": 5
- "n": 67108081
"n_hex": "0x3fffcf1"
"n_bit": "2^26 - 2^10 + 2^8 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5 * 13 * 137 * 157 + 1"
"nd": 7113711
"nd_hex": "0x6c8bef"
"nd_bit": "2^23 - 2^20 - 2^18 + 2^15 + 2^12 - 2^10 - 2^4 - 1"
"r2": 613089
"r2_hex": "0x95ae1"
"r2_bit": "2^19 + 2^17 - 2^15 - 2^13 - 2^10 - 2^8 - 2^5 + 1"
"znprimroot": 7
- "n": 67102561
"n_hex": "0x3ffe761"
"n_bit": "2^26 - 2^13 + 2^11 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5 * 7^2 * 317 + 1"
"nd": 3343199
"nd_hex": "0x33035f"
"nd_bit": "2^22 - 2^20 + 2^18 - 2^16 + 2^10 - 2^7 - 2^5 - 1"
"r2": 39727809
"r2_hex": "0x25e32c1"
"r2_bit": "2^25 + 2^23 - 2^21 - 2^17 + 2^14 - 2^12 + 2^10 - 2^8 - 2^6 + 1"
"znprimroot": 13
- "n": 67108289
"n_hex": "0x3fffdc1"
"n_bit": "2^26 - 2^9 - 2^6 + 1"
"n_fac": "2^6 * 13 * 79 * 1021 + 1"
"nd": 60222911
"nd_hex": "0x396edbf"
"nd_bit": "2^26 - 2^23 + 2^21 - 2^19 - 2^16 - 2^12 - 2^9 - 2^6 - 1"
"r2": 330625
"r2_hex": "0x50b81"
"r2_bit": "2^18 + 2^16 + 2^12 - 2^10 - 2^7 + 1"
"znprimroot": 6
- "n": 67108033
"n_hex": "0x3fffcc1"
"n_bit": "2^26 - 2^10 + 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3^2 * 116507 + 1"
"nd": 10579135
"nd_hex": "0xa16cbf"
"nd_bit": "2^23 + 2^21 + 2^17 - 2^15 - 2^12 - 2^10 + 2^8 - 2^6 - 1"
"r2": 690561
"r2_hex": "0xa8981"
"r2_bit": "2^19 + 2^17 + 2^15 + 2^11 + 2^9 - 2^7 + 1"
"znprimroot": 5
- "n": 67097281
"n_hex": "0x3ffd2c1"
"n_bit": "2^26 - 2^14 + 2^12 + 2^10 - 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 37 * 1889 + 1"
"nd": 46940863
"nd_hex": "0x2cc42bf"
"nd_bit": "2^26 - 2^24 - 2^22 + 2^20 - 2^18 + 2^14 + 2^10 - 2^8 - 2^6 - 1"
"r2": 67068608
"r2_hex": "0x3ff62c0"
"r2_bit": "2^26 - 2^15 - 2^13 + 2^10 - 2^8 - 2^6"
"znprimroot": 7
- "n": 67085761
"n_hex": "0x3ffa5c1"
"n_bit": "2^26 - 2^15 + 2^13 + 2^11 - 2^9 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 7 * 67 * 149 + 1"
"nd": 55219647
"nd_hex": "0x34a95bf"
"nd_bit": "2^26 - 2^24 + 2^22 + 2^19 + 2^17 + 2^15 + 2^13 - 2^11 - 2^9 - 2^6 - 1"
"r2": 64148282
"r2_hex": "0x3d2d33a"
"r2_bit": "2^26 - 2^22 + 2^20 + 2^18 - 2^16 - 2^14 + 2^12 + 2^10 - 2^8 + 2^6 - 2^3 + 2"
"znprimroot": 19
- "n": 67107713
"n_hex": "0x3fffb81"
"n_bit": "2^26 - 2^10 - 2^7 + 1"
"n_fac": "2^7 * 7 * 74897 + 1"
"nd": 13351807
"nd_hex": "0xcbbb7f"
"nd_bit": "2^24 - 2^22 + 2^20 - 2^18 - 2^14 - 2^10 - 2^7 - 1"
"r2": 1324801
"r2_hex": "0x143701"
"r2_bit": "2^20 + 2^18 + 2^14 - 2^11 - 2^8 + 1"
"znprimroot": 3
- "n": 67107457
"n_hex": "0x3fffa81"
"n_bit": "2^26 - 2^11 + 2^9 + 2^7 + 1"
"n_fac": "2^7 * 3^2 * 13 * 4481 + 1"
"nd": 25279103
"nd_hex": "0x181ba7f"
"nd_bit": "2^25 - 2^23 + 2^17 - 2^14 - 2^11 + 2^9 + 2^7 - 1"
"r2": 1979649
"r2_hex": "0x1e3501"
"r2_bit": "2^21 - 2^17 + 2^14 - 2^12 + 2^10 + 2^8 + 1"
"znprimroot": 5
- "n": 67090561
"n_hex": "0x3ffb881"
"n_bit": "2^26 - 2^14 - 2^11 + 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 83 * 421 + 1"
"nd": 36141183
"nd_hex": "0x227787f"
"nd_bit": "2^25 + 2^21 + 2^19 - 2^15 - 2^11 + 2^7 - 1"
"r2": 66637565
"r2_hex": "0x3f8cefd"
"r2_bit": "2^26 - 2^19 + 2^16 - 2^14 + 2^12 - 2^8 - 2^2 + 1"
"znprimroot": 7
- "n": 67079041
"n_hex": "0x3ff8b81"
"n_bit": "2^26 - 2^15 + 2^12 - 2^10 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 7^2 * 23 * 31 + 1"
"nd": 64703359
"nd_hex": "0x3db4b7f"
"nd_bit": "2^26 - 2^21 - 2^18 - 2^16 + 2^14 + 2^12 - 2^10 - 2^7 - 1"
"r2": 17383796
"r2_hex": "0x1094174"
"r2_bit": "2^24 + 2^19 + 2^16 + 2^14 + 2^9 - 2^7 - 2^4 + 2^2"
"znprimroot": 22
- "n": 67106561
"n_hex": "0x3fff701"
"n_bit": "2^26 - 2^11 - 2^8 + 1"
"n_fac": "2^8 * 5 * 103 * 509 + 1"
"nd": 45020927
"nd_hex": "0x2aef6ff"
"nd_bit": "2^26 - 2^24 - 2^22 - 2^20 - 2^16 - 2^11 - 2^8 - 1"
"r2": 5303809
"r2_hex": "0x50ee01"
"r2_bit": "2^22 + 2^20 + 2^16 - 2^12 - 2^9 + 1"
"znprimroot": 3
- "n": 66850561
"n_hex": "0x3fc0f01"
"n_bit": "2^26 - 2^18 + 2^12 - 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5 * 7 * 829 + 1"
"nd": 35327743
"nd_hex": "0x21b0eff"
"nd_bit": "2^25 + 2^21 - 2^18 - 2^16 + 2^12 - 2^8 - 1"
"r2": 3579931
"r2_hex": "0x36a01b"
"r2_bit": "2^22 - 2^19 - 2^17 + 2^15 + 2^13 + 2^5 - 2^2 - 1"
"znprimroot": 13
- "n": 67087873
"n_hex": "0x3ffae01"
"n_bit": "2^26 - 2^14 - 2^12 - 2^9 + 1"
"n_fac": "2^9 * 3^3 * 23 * 211 + 1"
"nd": 29076991
"nd_hex": "0x1bbadff"
"nd_bit": "2^25 - 2^22 - 2^18 - 2^14 - 2^12 - 2^9 - 1"
"r2": 38094843
"r2_hex": "0x24547fb"
"r2_bit": "2^25 + 2^22 + 2^18 + 2^16 + 2^14 + 2^11 - 2^2 - 1"
"znprimroot": 5
- "n": 67069441
"n_hex": "0x3ff6601"
"n_bit": "2^26 - 2^15 - 2^13 + 2^11 - 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5 * 41 * 71 + 1"
"nd": 56321535
"nd_hex": "0x35b65ff"
"nd_bit": "2^26 - 2^23 - 2^21 - 2^18 - 2^15 - 2^13 + 2^11 - 2^9 - 1"
"r2": 11575786
"r2_hex": "0xb0a1ea"
"r2_bit": "2^24 - 2^22 - 2^20 + 2^15 + 2^13 + 2^9 - 2^5 + 2^3 + 2"
"znprimroot": 7
- "n": 66823681
"n_hex": "0x3fba601"
"n_bit": "2^26 - 2^18 - 2^15 + 2^13 + 2^11 - 2^9 + 1"
"n_fac": "2^9 * 3 * 5 * 7 * 11 * 113 + 1"
"nd": 5744127
"nd_hex": "0x57a5ff"
"nd_bit": "2^23 - 2^21 - 2^19 - 2^15 + 2^13 + 2^11 - 2^9 - 1"
"r2": 4923712
"r2_hex": "0x4b2140"
"r2_bit": "2^22 + 2^20 - 2^18 - 2^16 + 2^13 + 2^8 + 2^6"
"znprimroot": 13
- "n": 65318401
"n_hex": "0x3e4ae01"
"n_bit": "2^26 - 2^21 + 2^18 + 2^16 - 2^14 - 2^12 - 2^9 + 1"
"n_fac": "2^9 * 3^6 * 5^2 * 7 + 1"
"nd": 27307519
"nd_hex": "0x1a0adff"
"nd_bit": "2^25 - 2^23 + 2^21 + 2^16 - 2^14 - 2^12 - 2^9 - 1"
"r2": 61270091
"r2_hex": "0x3a6e84b"
"r2_bit": "2^26 - 2^23 + 2^21 + 2^19 - 2^16 - 2^13 + 2^11 + 2^6 + 2^4 - 2^2 - 1"
"znprimroot": 13
- "n": 67046401
"n_hex": "0x3ff0c01"
"n_bit": "2^26 - 2^16 + 2^12 - 2^10 + 1"
"n_fac": "2^10 * 3^3 * 5^2 * 97 + 1"
"nd": 57609215
"nd_hex": "0x36f0bff"
"nd_bit": "2^26 - 2^23 - 2^20 - 2^16 + 2^12 - 2^10 - 1"
"r2": 12935111
"r2_hex": "0xc55fc7"
"r2_bit": "2^24 - 2^22 + 2^19 - 2^17 - 2^15 - 2^13 - 2^6 + 2^3 - 1"
"znprimroot": 19
- "n": 65157121
"n_hex": "0x3e23801"
"n_bit": "2^26 - 2^21 + 2^17 + 2^14 - 2^11 + 1"
"n_fac": "2^11 * 3^2 * 5 * 7 * 101 + 1"
"nd": 60962815
"nd_hex": "0x3a237ff"
"nd_bit": "2^26 - 2^23 + 2^21 + 2^17 + 2^14 - 2^11 - 1"
"r2": 19973026
"r2_hex": "0x130c3a2"
"r2_bit": "2^24 + 2^22 - 2^20 + 2^16 - 2^14 + 2^10 - 2^7 + 2^5 + 2"
"znprimroot": 23
- "n": 67104769
"n_hex": "0x3fff001"
"n_bit": "2^26 - 2^12 + 1"
"n_fac": "2^12 * 3 * 43 * 127 + 1"
"nd": 50327551
"nd_hex": "0x2ffefff"
"nd_bit": "2^26 - 2^24 - 2^12 - 1"
"r2": 16769025
"r2_hex": "0xffe001"
"r2_bit": "2^24 - 2^13 + 1"
"znprimroot": 17
- "n": 66908161
"n_hex": "0x3fcf001"
"n_bit": "2^26 - 2^18 + 2^16 - 2^12 + 1"
"n_fac": "2^12 * 3^3 * 5 * 11^2 + 1"
"nd": 50130943
"nd_hex": "0x2fcefff"
"nd_bit": "2^26 - 2^24 - 2^18 + 2^16 - 2^12 - 1"
"r2": 2981287
"r2_hex": "0x2d7da7"
"r2_bit": "2^22 - 2^20 - 2^17 - 2^15 - 2^9 - 2^7 + 2^5 + 2^3 - 1"
"znprimroot": 7
- "n": 64942081
"n_hex": "0x3def001"
"n_bit": "2^26 - 2^21 - 2^16 - 2^12 + 1"
"n_fac": "2^12 * 3 * 5 * 7 * 151 + 1"
"nd": 48164863
"nd_hex": "0x2deefff"
"nd_bit": "2^26 - 2^24 - 2^21 - 2^16 - 2^12 - 1"
"r2": 25765275
"r2_hex": "0x189259b"
"r2_bit": "2^25 - 2^23 + 2^19 + 2^16 + 2^13 + 2^11 - 2^9 - 2^7 + 2^5 - 2^2 - 1"
"znprimroot": 11
- "n": 67084289
"n_hex": "0x3ffa001"
"n_bit": "2^26 - 2^15 + 2^13 + 1"
"n_fac": "2^13 * 19 * 431 + 1"
"nd": 67084287
"nd_hex": "0x3ff9fff"
"nd_bit": "2^26 - 2^15 + 2^13 - 1"
"r2": 172024
"r2_hex": "0x29ff8"
"r2_bit": "2^17 + 2^15 + 2^13 - 2^3"
"znprimroot": 3
- "n": 66969601
"n_hex": "0x3fde001"
"n_bit": "2^26 - 2^17 - 2^13 + 1"
"n_fac": "2^13 * 3 * 5^2 * 109 + 1"
"nd": 66969599
"nd_hex": "0x3fddfff"
"nd_bit": "2^26 - 2^17 - 2^13 - 1"
"r2": 39968480
"r2_hex": "0x261dee0"
"r2_bit": "2^25 + 2^23 - 2^21 + 2^17 - 2^13 - 2^8 - 2^5"
"znprimroot": 7
- "n": 66723841
"n_hex": "0x3fa2001"
"n_bit": "2^26 - 2^19 + 2^17 + 2^13 + 1"
"n_fac": "2^13 * 3^2 * 5 * 181 + 1"
"nd": 66723839
"nd_hex": "0x3fa1fff"
"nd_bit": "2^26 - 2^19 + 2^17 + 2^13 - 1"
"r2": 49059668
"r2_hex": "0x2ec9754"
"r2_bit": "2^26 - 2^24 - 2^20 - 2^18 + 2^15 + 2^13 - 2^11 - 2^8 + 2^6 + 2^4 + 2^2"
"znprimroot": 11
- "n": 64512001
"n_hex": "0x3d86001"
"n_bit": "2^26 - 2^21 - 2^19 + 2^15 - 2^13 + 1"
"n_fac": "2^13 * 3^2 * 5^3 * 7 + 1"
"nd": 64511999
"nd_hex": "0x3d85fff"
"nd_bit": "2^26 - 2^21 - 2^19 + 2^15 - 2^13 - 1"
"r2": 64440236
"r2_hex": "0x3d747ac"
"r2_bit": "2^26 - 2^21 - 2^19 - 2^16 + 2^14 + 2^11 - 2^6 - 2^4 - 2^2"
"znprimroot": 13
- "n": 65028097
"n_hex": "0x3e04001"
"n_bit": "2^26 - 2^21 + 2^14 + 1"
"n_fac": "2^14 * 3^4 * 7^2 + 1"
"nd": 65028095
"nd_hex": "0x3e03fff"
"nd_bit": "2^26 - 2^21 + 2^14 - 1"
"r2": 20610029
"r2_hex": "0x13a7bed"
"r2_bit": "2^24 + 2^22 - 2^19 + 2^17 + 2^15 - 2^10 - 2^4 - 2^2 + 1"
"znprimroot": 10
- "n": 60211201
"n_hex": "0x396c001"
"n_bit": "2^26 - 2^23 + 2^21 - 2^19 - 2^16 - 2^14 + 1"
"n_fac": "2^14 * 3 * 5^2 * 7^2 + 1"
"nd": 60211199
"nd_hex": "0x396bfff"
"nd_bit": "2^26 - 2^23 + 2^21 - 2^19 - 2^16 - 2^14 - 1"
"r2": 7844188
"r2_hex": "0x77b15c"
"r2_bit": "2^23 - 2^19 - 2^14 - 2^12 + 2^9 - 2^7 - 2^5 - 2^2"
"znprimroot": 13
- "n": 56770561
"n_hex": "0x3624001"
"n_bit": "2^26 - 2^23 - 2^21 + 2^17 + 2^14 + 1"
"n_fac": "2^14 * 3^2 * 5 * 7 * 11 + 1"
"nd": 56770559
"nd_hex": "0x3623fff"
"nd_bit": "2^26 - 2^23 - 2^21 + 2^17 + 2^14 - 1"
"r2": 49759695
"r2_hex": "0x2f745cf"
"r2_bit": "2^26 - 2^24 - 2^19 - 2^16 + 2^14 + 2^11 - 2^9 - 2^6 + 2^4 - 1"
"znprimroot": 31
- "n": 60456961
"n_hex": "0x39a8001"
"n_bit": "2^26 - 2^23 + 2^21 - 2^19 + 2^17 + 2^15 + 1"
"n_fac": "2^15 * 3^2 * 5 * 41 + 1"
"nd": 60456959
"nd_hex": "0x39a7fff"
"nd_bit": "2^26 - 2^23 + 2^21 - 2^19 + 2^17 + 2^15 - 1"
"r2": 28792080
"r2_hex": "0x1b75510"
"r2_bit": "2^25 - 2^22 - 2^19 - 2^16 + 2^14 + 2^12 + 2^10 + 2^8 + 2^4"
"znprimroot": 7
- "n": 58490881
"n_hex": "0x37c8001"
"n_bit": "2^26 - 2^23 - 2^18 + 2^15 + 1"
"n_fac": "2^15 * 3 * 5 * 7 * 17 + 1"
"nd": 58490879
"nd_hex": "0x37c7fff"
"nd_bit": "2^26 - 2^23 - 2^18 + 2^15 - 1"
"r2": 15966205
"r2_hex": "0xf39ffd"
"r2_bit": "2^24 - 2^20 + 2^18 - 2^15 + 2^13 - 2^2 + 1"
"znprimroot": 26
- "n": 30965761
"n_hex": "0x1d88001"
"n_bit": "2^25 - 2^21 - 2^19 + 2^15 + 1"
"n_fac": "2^15 * 3^3 * 5 * 7 + 1"
"nd": 30965759
"nd_hex": "0x1d87fff"
"nd_bit": "2^25 - 2^21 - 2^19 + 2^15 - 1"
"r2": 9456295
"r2_hex": "0x904aa7"
"r2_bit": "2^23 + 2^20 + 2^14 + 2^11 + 2^9 + 2^7 + 2^5 + 2^3 - 1"
"znprimroot": 39
- "n": 67043329
"n_hex": "0x3ff0001"
"n_bit": "2^26 - 2^16 + 1"
"n_fac": "2^16 * 3 * 11 * 31 + 1"
"nd": 67043327
"nd_hex": "0x3feffff"
"nd_bit": "2^26 - 2^16 - 1"
"r2": 4063169
"r2_hex": "0x3dffc1"
"r2_bit": "2^22 - 2^17 - 2^6 + 1"
"znprimroot": 7
- "n": 63897601
"n_hex": "0x3cf0001"
"n_bit": "2^26 - 2^22 + 2^20 - 2^16 + 1"
"n_fac": "2^16 * 3 * 5^2 * 13 + 1"
"nd": 63897599
"nd_hex": "0x3ceffff"
"nd_bit": "2^26 - 2^22 + 2^20 - 2^16 - 1"
"r2": 31820183
"r2_hex": "0x1e58997"
"r2_bit": "2^25 - 2^21 + 2^19 - 2^17 - 2^15 + 2^11 + 2^9 - 2^7 + 2^5 - 2^3 - 1"
"znprimroot": 7
- "n": 48168961
"n_hex": "0x2df0001"
"n_bit": "2^26 - 2^24 - 2^21 - 2^16 + 1"
"n_fac": "2^16 * 3 * 5 * 7^2 + 1"
"nd": 48168959
"nd_hex": "0x2deffff"
"nd_bit": "2^26 - 2^24 - 2^21 - 2^16 - 1"
"r2": 37313972
"r2_hex": "0x2395db4"
"r2_bit": "2^25 + 2^22 - 2^19 + 2^17 - 2^15 - 2^13 - 2^9 - 2^6 - 2^4 + 2^2"
"znprimroot": 17
- "n": 65929217
"n_hex": "0x3ee0001"
"n_bit": "2^26 - 2^20 - 2^17 + 1"
"n_fac": "2^17 * 503 + 1"
"nd": 65929215
"nd_hex": "0x3edffff"
"nd_bit": "2^26 - 2^20 - 2^17 - 1"
"r2": 64990607
"r2_hex": "0x3dfad8f"
"r2_bit": "2^26 - 2^21 - 2^14 - 2^12 - 2^9 - 2^7 + 2^4 - 1"
"znprimroot": 3
- "n": 49152001
"n_hex": "0x2ee0001"
"n_bit": "2^26 - 2^24 - 2^20 - 2^17 + 1"
"n_fac": "2^17 * 3 * 5^3 + 1"
"nd": 49151999
"nd_hex": "0x2edffff"
"nd_bit": "2^26 - 2^24 - 2^20 - 2^17 - 1"
"r2": 5760529
"r2_hex": "0x57e611"
"r2_bit": "2^23 - 2^21 - 2^19 - 2^13 + 2^11 - 2^9 + 2^4 + 1"
"znprimroot": 7
- "n": 64749569
"n_hex": "0x3dc0001"
"n_bit": "2^26 - 2^21 - 2^18 + 1"
"n_fac": "2^18 * 13 * 19 + 1"
"nd": 64749567
"nd_hex": "0x3dbffff"
"nd_bit": "2^26 - 2^21 - 2^18 - 1"
"r2": 11448371
"r2_hex": "0xaeb033"
"r2_bit": "2^24 - 2^22 - 2^20 - 2^16 - 2^14 - 2^12 + 2^6 - 2^4 + 2^2 - 1"
"znprimroot": 6
- "n": 63700993
"n_hex": "0x3cc0001"
"n_bit": "2^26 - 2^22 + 2^20 - 2^18 + 1"
"n_fac": "2^18 * 3^5 + 1"
"nd": 63700991
"nd_hex": "0x3cbffff"
"nd_bit": "2^26 - 2^22 + 2^20 - 2^18 - 1"
"r2": 1914839
"r2_hex": "0x1d37d7"
"r2_bit": "2^21 - 2^18 + 2^16 + 2^14 - 2^11 - 2^5 - 2^3 - 1"
"znprimroot": 5
- "n": 35389441
"n_hex": "0x21c0001"
"n_bit": "2^25 + 2^21 - 2^18 + 1"
"n_fac": "2^18 * 3^3 * 5 + 1"
"nd": 35389439
"nd_hex": "0x21bffff"
"nd_bit": "2^25 + 2^21 - 2^18 - 1"
"r2": 23212370
"r2_hex": "0x1623152"
"r2_bit": "2^25 - 2^23 - 2^21 + 2^17 + 2^14 - 2^12 + 2^8 + 2^6 + 2^4 + 2"
"znprimroot": 7
- "n": 40370177
"n_hex": "0x2680001"
"n_bit": "2^25 + 2^23 - 2^21 + 2^19 + 1"
"n_fac": "2^19 * 7 * 11 + 1"
"nd": 40370175
"nd_hex": "0x267ffff"
"nd_bit": "2^25 + 2^23 - 2^21 + 2^19 - 1"
"r2": 13747243
"r2_hex": "0xd1c42b"
"r2_bit": "2^24 - 2^22 + 2^20 + 2^17 - 2^14 + 2^10 + 2^6 - 2^4 - 2^2 - 1"
"znprimroot": 3
- "n": 36175873
"n_hex": "0x2280001"
"n_bit": "2^25 + 2^21 + 2^19 + 1"
"n_fac": "2^19 * 3 * 23 + 1"
"nd": 36175871
"nd_hex": "0x227ffff"
"nd_bit": "2^25 + 2^21 + 2^19 - 1"
"r2": 8677350
"r2_hex": "0x8467e6"
"r2_bit": "2^23 + 2^18 + 2^15 - 2^13 + 2^11 - 2^5 + 2^3 - 2"
"znprimroot": 7
- "n": 28311553
"n_hex": "0x1b00001"
"n_bit": "2^25 - 2^22 - 2^20 + 1"
"n_fac": "2^20 * 3^3 + 1"
"nd": 28311551
"nd_hex": "0x1afffff"
"nd_bit": "2^25 - 2^22 - 2^20 - 1"
"r2": 5553575
"r2_hex": "0x54bda7"
"r2_bit": "2^22 + 2^20 + 2^18 + 2^16 - 2^14 - 2^9 - 2^7 + 2^5 + 2^3 - 1"
"znprimroot": 5
- "n": 23068673
"n_hex": "0x1600001"
"n_bit": "2^25 - 2^23 - 2^21 + 1"
"n_fac": "2^21 * 11 + 1"
"nd": 23068671
"nd_hex": "0x15fffff"
"nd_bit": "2^25 - 2^23 - 2^21 - 1"
"r2": 16586575
"r2_hex": "0xfd174f"
"r2_bit": "2^24 - 2^18 + 2^16 + 2^13 - 2^11 - 2^8 + 2^6 + 2^4 - 1"
"znprimroot": 3
Raw
result_prime_0030.yaml
- "r": 30
"primes":
- "n": 1073741719
"n_hex": "0x3fffff97"
"n_bit": "2^30 - 2^7 + 2^5 - 2^3 - 1"
"n_fac": "2 * 3 * 7 * 19 * 1345541 + 1"
"nd": 419270617
"nd_hex": "0x18fd8fd9"
"nd_bit": "2^29 - 2^27 + 2^24 - 2^17 - 2^15 + 2^12 - 2^5 - 2^3 + 1"
"r2": 11025
"r2_hex": "0x2b11"
"r2_bit": "2^14 - 2^12 - 2^10 - 2^8 + 2^4 + 1"
"znprimroot": 6
- "n": 1073741671
"n_hex": "0x3fffff67"
"n_bit": "2^30 - 2^7 - 2^5 + 2^3 - 1"
"n_fac": "2 * 3^5 * 5 * 73 * 6053 + 1"
"nd": 687756201
"nd_hex": "0x28fe53a9"
"nd_bit": "2^29 + 2^27 + 2^24 - 2^17 + 2^14 + 2^12 + 2^10 - 2^7 + 2^5 + 2^3 + 1"
"r2": 23409
"r2_hex": "0x5b71"
"r2_bit": "2^15 - 2^13 - 2^10 - 2^7 - 2^4 + 1"
"znprimroot": 6
- "n": 1073741789
"n_hex": "0x3fffffdd"
"n_bit": "2^30 - 2^5 - 2^2 + 1"
"n_fac": "2^2 * 7 * 2341 * 16381 + 1"
"nd": 184070027
"nd_hex": "0xaf8af8b"
"nd_bit": "2^28 - 2^26 - 2^24 - 2^19 + 2^16 - 2^14 - 2^12 - 2^7 + 2^4 - 2^2 - 1"
"r2": 1225
"r2_hex": "0x4c9"
"r2_bit": "2^10 + 2^8 - 2^6 + 2^3 + 1"
"znprimroot": 2
- "n": 1073741101
"n_hex": "0x3ffffd2d"
"n_bit": "2^30 - 2^10 + 2^8 + 2^6 - 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3 * 5^2 * 101 * 35437 + 1"
"nd": 452961627
"nd_hex": "0x1affa55b"
"nd_bit": "2^29 - 2^26 - 2^24 - 2^15 + 2^13 + 2^11 - 2^9 - 2^7 - 2^5 - 2^2 - 1"
"r2": 522729
"r2_hex": "0x7f9e9"
"r2_bit": "2^19 - 2^11 + 2^9 - 2^5 + 2^3 + 1"
"znprimroot": 10
- "n": 1073740501
"n_hex": "0x3ffffad5"
"n_bit": "2^30 - 2^10 - 2^8 - 2^6 + 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5^3 * 7 * 89 * 383 + 1"
"nd": 254841219
"nd_hex": "0xf309183"
"nd_bit": "2^28 - 2^24 + 2^22 - 2^20 + 2^15 + 2^12 + 2^9 - 2^7 + 2^2 - 1"
"r2": 1750329
"r2_hex": "0x1ab539"
"r2_bit": "2^21 - 2^18 - 2^16 - 2^14 - 2^12 + 2^10 + 2^8 + 2^6 - 2^3 + 1"
"znprimroot": 6
- "n": 1073741689
"n_hex": "0x3fffff79"
"n_bit": "2^30 - 2^7 - 2^3 + 1"
"n_fac": "2^3 * 3^2 * 14913079 + 1"
"nd": 564708663
"nd_hex": "0x21a8c537"
"nd_bit": "2^29 + 2^25 - 2^23 + 2^21 + 2^19 + 2^16 - 2^14 + 2^10 + 2^8 + 2^6 - 2^3 - 1"
"r2": 18225
"r2_hex": "0x4731"
"r2_bit": "2^14 + 2^11 - 2^8 + 2^6 - 2^4 + 1"
"znprimroot": 13
- "n": 1073740201
"n_hex": "0x3ffff9a9"
"n_bit": "2^30 - 2^11 + 2^9 - 2^7 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5^2 * 13 * 137659 + 1"
"nd": 922240359
"nd_hex": "0x36f84567"
"nd_bit": "2^30 - 2^27 - 2^24 - 2^19 + 2^14 + 2^11 - 2^9 - 2^7 - 2^5 + 2^3 - 1"
"r2": 2634129
"r2_hex": "0x283191"
"r2_bit": "2^21 + 2^19 + 2^14 - 2^12 + 2^9 - 2^7 + 2^4 + 1"
"znprimroot": 11
- "n": 1073738521
"n_hex": "0x3ffff319"
"n_bit": "2^30 - 2^12 + 2^10 - 2^8 + 2^5 - 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5 * 37 * 80611 + 1"
"nd": 341984983
"nd_hex": "0x146246d7"
"nd_bit": "2^28 + 2^26 + 2^23 - 2^21 + 2^17 + 2^14 + 2^11 - 2^8 - 2^5 - 2^3 - 1"
"r2": 10909809
"r2_hex": "0xa67871"
"r2_bit": "2^23 + 2^21 + 2^19 - 2^17 + 2^15 - 2^11 + 2^7 - 2^4 + 1"
"znprimroot": 13
- "n": 1073734201
"n_hex": "0x3fffe239"
"n_bit": "2^30 - 2^13 + 2^9 + 2^6 - 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5^2 * 7 * 11 * 61 * 127 + 1"
"nd": 585536503
"nd_hex": "0x22e693f7"
"nd_bit": "2^29 + 2^26 - 2^24 - 2^21 + 2^19 - 2^17 + 2^15 + 2^12 + 2^10 - 2^3 - 1"
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"nd_bit": "2^30 - 2^28 + 2^26 + 2^23 - 1"
"r2": 469442484
"r2_hex": "0x1bfb1fb4"
"r2_bit": "2^29 - 2^26 - 2^18 - 2^16 + 2^13 - 2^6 - 2^4 + 2^2"
"znprimroot": 26
- "n": 754974721
"n_hex": "0x2d000001"
"n_bit": "2^30 - 2^28 - 2^26 + 2^24 + 1"
"n_fac": "2^24 * 3^2 * 5 + 1"
"nd": 754974719
"nd_hex": "0x2cffffff"
"nd_bit": "2^30 - 2^28 - 2^26 + 2^24 - 1"
"r2": 754601896
"r2_hex": "0x2cfa4fa8"
"r2_bit": "2^30 - 2^28 - 2^26 + 2^24 - 2^19 + 2^17 + 2^14 + 2^12 - 2^7 + 2^5 + 2^3"
"znprimroot": 11
- "n": 469762049
"n_hex": "0x1c000001"
"n_bit": "2^29 - 2^26 + 1"
"n_fac": "2^26 * 7 + 1"
"nd": 469762047
"nd_hex": "0x1bffffff"
"nd_bit": "2^29 - 2^26 - 1"
"r2": 28760947
"r2_hex": "0x1b6db73"
"r2_bit": "2^25 - 2^22 - 2^19 - 2^16 - 2^13 - 2^10 - 2^7 - 2^4 + 2^2 - 1"
"znprimroot": 3
Raw
result_prime_0031.yaml
- "r": 31
"primes":
- "n": 2147483647
"n_hex": "0x7fffffff"
"n_bit": "2^31 - 1"
"n_fac": "2 * 3^2 * 7 * 11 * 31 * 151 * 331 + 1"
"nd": 1
"nd_hex": "0x1"
"nd_bit": "1"
"r2": 1
"r2_hex": "0x1"
"r2_bit": "1"
"znprimroot": 7
- "n": 2147482951
"n_hex": "0x7ffffd47"
"n_bit": "2^31 - 2^10 + 2^8 + 2^6 + 2^3 - 1"
"n_fac": "2 * 3 * 5^2 * 14316553 + 1"
"nd": 569992073
"nd_hex": "0x21f96389"
"nd_bit": "2^29 + 2^25 - 2^19 + 2^17 - 2^15 - 2^13 + 2^10 - 2^7 + 2^3 + 1"
"r2": 485809
"r2_hex": "0x769b1"
"r2_bit": "2^19 - 2^15 - 2^13 + 2^11 + 2^9 - 2^6 - 2^4 + 1"
"znprimroot": 6
- "n": 2147483629
"n_hex": "0x7fffffed"
"n_bit": "2^31 - 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 59652323 + 1"
"nd": 678152731
"nd_hex": "0x286bca1b"
"nd_bit": "2^29 + 2^27 + 2^23 - 2^20 - 2^18 - 2^14 + 2^11 + 2^9 + 2^5 - 2^2 - 1"
"r2": 361
"r2_hex": "0x169"
"r2_bit": "2^9 - 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 2
- "n": 2147483497
"n_hex": "0x7fffff69"
"n_bit": "2^31 - 2^7 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 277 * 323027 + 1"
"nd": 1066630951
"nd_hex": "0x3f937f27"
"nd_bit": "2^30 - 2^23 + 2^20 + 2^18 - 2^15 - 2^8 + 2^5 + 2^3 - 1"
"r2": 22801
"r2_hex": "0x5911"
"r2_bit": "2^15 - 2^13 - 2^11 + 2^8 + 2^4 + 1"
"znprimroot": 5
- "n": 2147482921
"n_hex": "0x7ffffd29"
"n_bit": "2^31 - 2^10 + 2^8 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 11 * 1626881 + 1"
"nd": 1420824807
"nd_hex": "0x54b010e7"
"nd_bit": "2^30 + 2^28 + 2^26 + 2^24 - 2^22 - 2^20 + 2^12 + 2^8 - 2^5 + 2^3 - 1"
"r2": 528529
"r2_hex": "0x81091"
"r2_bit": "2^19 + 2^12 + 2^7 + 2^4 + 1"
"znprimroot": 21
- "n": 2147482873
"n_hex": "0x7ffffcf9"
"n_bit": "2^31 - 2^10 + 2^8 - 2^3 + 1"
"n_fac": "2^3 * 3^2 * 4451 * 6701 + 1"
"nd": 728758967
"nd_hex": "0x2b6ffab7"
"nd_bit": "2^30 - 2^28 - 2^26 - 2^23 - 2^20 - 2^10 - 2^8 - 2^6 - 2^3 - 1"
"r2": 600625
"r2_hex": "0x92a31"
"r2_bit": "2^19 + 2^16 + 2^13 + 2^11 + 2^9 + 2^6 - 2^4 + 1"
"znprimroot": 11
- "n": 2147482681
"n_hex": "0x7ffffc39"
"n_bit": "2^31 - 2^10 + 2^6 - 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 7 * 1093 * 2339 + 1"
"nd": 257609207
"nd_hex": "0xf5acdf7"
"nd_bit": "2^28 - 2^23 - 2^21 - 2^18 - 2^16 - 2^14 + 2^12 - 2^9 - 2^3 - 1"
"r2": 935089
"r2_hex": "0xe44b1"
"r2_bit": "2^20 - 2^17 + 2^14 + 2^10 + 2^8 - 2^6 - 2^4 + 1"
"znprimroot": 13
- "n": 2147482801
"n_hex": "0x7ffffcb1"
"n_bit": "2^31 - 2^10 + 2^8 - 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3^3 * 5^2 * 198841 + 1"
"nd": 2048603055
"nd_hex": "0x7a1b33af"
"nd_bit": "2^31 - 2^27 + 2^25 + 2^21 - 2^18 - 2^16 + 2^14 - 2^12 + 2^10 - 2^6 - 2^4 - 1"
"r2": 717409
"r2_hex": "0xaf261"
"r2_bit": "2^20 - 2^18 - 2^16 - 2^12 + 2^9 + 2^7 - 2^5 + 1"
"znprimroot": 22
- "n": 2147478481
"n_hex": "0x7fffebd1"
"n_bit": "2^31 - 2^12 - 2^10 - 2^6 + 2^4 + 1"
"n_fac": "2^4 * 3^5 * 5 * 7 * 43 * 367 + 1"
"nd": 935965391
"nd_hex": "0x37c9b2cf"
"nd_bit": "2^30 - 2^27 - 2^22 + 2^19 + 2^17 - 2^14 - 2^12 + 2^10 - 2^8 - 2^6 + 2^4 - 1"
"r2": 26697889
"r2_hex": "0x19760a1"
"r2_bit": "2^25 - 2^23 + 2^21 - 2^19 - 2^15 - 2^13 + 2^7 + 2^5 + 1"
"znprimroot": 13
- "n": 2147483489
"n_hex": "0x7fffff61"
"n_bit": "2^31 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 67108859 + 1"
"nd": 783358815
"nd_hex": "0x2eb11b5f"
"nd_bit": "2^30 - 2^28 - 2^24 - 2^22 - 2^20 + 2^16 + 2^13 - 2^10 - 2^7 - 2^5 - 1"
"r2": 25281
"r2_hex": "0x62c1"
"r2_bit": "2^15 - 2^13 + 2^10 - 2^8 - 2^6 + 1"
"znprimroot": 3
- "n": 2147482081
"n_hex": "0x7ffff9e1"
"n_bit": "2^31 - 2^11 + 2^9 - 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 911 * 1637 + 1"
"nd": 201455071
"nd_hex": "0xc01f5df"
"nd_bit": "2^28 - 2^26 + 2^17 - 2^11 - 2^9 - 2^5 - 1"
"r2": 2455489
"r2_hex": "0x2577c1"
"r2_bit": "2^21 + 2^19 - 2^17 - 2^15 - 2^11 - 2^6 + 1"
"znprimroot": 11
- "n": 2147480161
"n_hex": "0x7ffff261"
"n_bit": "2^31 - 2^12 + 2^9 + 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 7 * 29 * 22039 + 1"
"nd": 1927007839
"nd_hex": "0x72dbce5f"
"nd_bit": "2^31 - 2^28 + 2^26 - 2^24 - 2^21 - 2^18 - 2^14 + 2^12 - 2^9 + 2^7 - 2^5 - 1"
"r2": 12159169
"r2_hex": "0xb988c1"
"r2_bit": "2^24 - 2^22 - 2^19 + 2^17 - 2^15 + 2^11 + 2^8 - 2^6 + 1"
"znprimroot": 19
- "n": 2147481793
"n_hex": "0x7ffff8c1"
"n_bit": "2^31 - 2^11 + 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3^2 * 3728267 + 1"
"nd": 1907845311
"nd_hex": "0x71b768bf"
"nd_bit": "2^31 - 2^28 + 2^25 - 2^22 - 2^19 - 2^15 - 2^13 + 2^11 + 2^8 - 2^6 - 1"
"r2": 3441025
"r2_hex": "0x348181"
"r2_bit": "2^22 - 2^20 + 2^18 + 2^15 + 2^9 - 2^7 + 1"
"znprimroot": 5
- "n": 2147480641
"n_hex": "0x7ffff441"
"n_bit": "2^31 - 2^12 + 2^10 + 2^6 + 1"
"n_fac": "2^6 * 3^3 * 5 * 199 * 1249 + 1"
"nd": 674882623
"nd_hex": "0x2839e43f"
"nd_bit": "2^29 + 2^27 + 2^22 - 2^19 + 2^17 - 2^13 + 2^10 + 2^6 - 1"
"r2": 9042049
"r2_hex": "0x89f881"
"r2_bit": "2^23 + 2^19 + 2^17 - 2^11 + 2^7 + 1"
"znprimroot": 7
- "n": 2147463361
"n_hex": "0x7fffb0c1"
"n_bit": "2^31 - 2^14 - 2^12 + 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3^3 * 5 * 7 * 35507 + 1"
"nd": 266543295
"nd_hex": "0xfe320bf"
"nd_bit": "2^28 - 2^21 + 2^18 - 2^16 + 2^13 + 2^8 - 2^6 - 1"
"r2": 411562369
"r2_hex": "0x1887f181"
"r2_bit": "2^29 - 2^27 + 2^23 + 2^19 - 2^12 + 2^9 - 2^7 + 1"
"znprimroot": 22
- "n": 2147479681
"n_hex": "0x7ffff081"
"n_bit": "2^31 - 2^12 + 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 1118479 + 1"
"nd": 1664069759
"nd_hex": "0x632fb07f"
"nd_bit": "2^31 - 2^29 + 2^26 - 2^24 + 2^22 - 2^20 - 2^14 - 2^12 + 2^7 - 1"
"r2": 15737089
"r2_hex": "0xf02101"
"r2_bit": "2^24 - 2^20 + 2^13 + 2^8 + 1"
"znprimroot": 22
- "n": 2147467393
"n_hex": "0x7fffc081"
"n_bit": "2^31 - 2^14 + 2^7 + 1"
"n_fac": "2^7 * 3^2 * 7 * 283 * 941 + 1"
"nd": 811565183
"nd_hex": "0x305f807f"
"nd_bit": "2^30 - 2^28 + 2^23 - 2^21 - 2^15 + 2^7 - 1"
"r2": 264225025
"r2_hex": "0xfbfc101"
"r2_bit": "2^28 - 2^22 - 2^14 + 2^8 + 1"
"znprimroot": 10
- "n": 2147470081
"n_hex": "0x7fffcb01"
"n_bit": "2^31 - 2^14 + 2^12 - 2^10 - 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 7^2 * 101 * 113 + 1"
"nd": 1745275647
"nd_hex": "0x6806caff"
"nd_bit": "2^31 - 2^29 + 2^27 + 2^19 - 2^16 - 2^14 + 2^12 - 2^10 - 2^8 - 1"
"r2": 184063489
"r2_hex": "0xaf89601"
"r2_bit": "2^28 - 2^26 - 2^24 - 2^19 + 2^15 + 2^13 - 2^11 - 2^9 + 1"
"znprimroot": 19
- "n": 2147450113
"n_hex": "0x7fff7d01"
"n_bit": "2^31 - 2^15 - 2^10 + 2^8 + 1"
"n_fac": "2^8 * 3^2 * 41 * 127 * 179 + 1"
"nd": 569801983
"nd_hex": "0x21f67cff"
"nd_bit": "2^29 + 2^25 - 2^19 - 2^17 + 2^15 - 2^10 + 2^8 - 1"
"r2": 1124596225
"r2_hex": "0x4307fa01"
"r2_bit": "2^30 + 2^26 - 2^24 + 2^19 - 2^11 + 2^9 + 1"
"znprimroot": 5
- "n": 2147431681
"n_hex": "0x7fff3501"
"n_bit": "2^31 - 2^16 + 2^14 - 2^12 + 2^10 + 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5 * 19 * 9811 + 1"
"nd": 1812346111
"nd_hex": "0x6c0634ff"
"nd_bit": "2^31 - 2^28 - 2^26 + 2^19 - 2^17 + 2^14 - 2^12 + 2^10 + 2^8 - 1"
"r2": 553137408
"r2_hex": "0x20f83500"
"r2_bit": "2^29 + 2^24 - 2^19 + 2^14 - 2^12 + 2^10 + 2^8"
"znprimroot": 7
- "n": 2147362561
"n_hex": "0x7ffe2701"
"n_bit": "2^31 - 2^17 + 2^13 + 2^11 - 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5 * 7 * 31 * 859 + 1"
"nd": 1292707583
"nd_hex": "0x4d0d26ff"
"nd_bit": "2^30 + 2^28 - 2^26 + 2^24 + 2^20 - 2^18 + 2^16 + 2^13 + 2^11 - 2^8 - 1"
"r2": 1777886203
"r2_hex": "0x69f863fb"
"r2_bit": "2^31 - 2^29 + 2^27 + 2^25 - 2^19 + 2^15 - 2^13 + 2^10 - 2^2 - 1"
"znprimroot": 13
- "n": 2147483137
"n_hex": "0x7ffffe01"
"n_bit": "2^31 - 2^9 + 1"
"n_fac": "2^9 * 3 * 23 * 89 * 683 + 1"
"nd": 2013003263
"nd_hex": "0x77fbfdff"
"nd_bit": "2^31 - 2^27 - 2^18 - 2^9 - 1"
"r2": 261121
"r2_hex": "0x3fc01"
"r2_bit": "2^18 - 2^10 + 1"
"znprimroot": 10
- "n": 2147473921
"n_hex": "0x7fffda01"
"n_bit": "2^31 - 2^13 - 2^11 + 2^9 + 1"
"n_fac": "2^9 * 3 * 5 * 279619 + 1"
"nd": 576444927
"nd_hex": "0x225bd9ff"
"nd_bit": "2^29 + 2^25 + 2^23 - 2^21 - 2^18 - 2^13 - 2^11 + 2^9 - 1"
"r2": 94614529
"r2_hex": "0x5a3b401"
"r2_bit": "2^27 - 2^25 - 2^23 + 2^21 + 2^18 - 2^14 - 2^12 + 2^10 + 1"
"znprimroot": 11
- "n": 2147415553
"n_hex": "0x7ffef601"
"n_bit": "2^31 - 2^16 - 2^11 - 2^9 + 1"
"n_fac": "2^9 * 3^2 * 466019 + 1"
"nd": 60487167
"nd_hex": "0x39af5ff"
"nd_bit": "2^26 - 2^23 + 2^21 - 2^18 - 2^16 - 2^11 - 2^9 - 1"
"r2": 342097919
"r2_hex": "0x1463ffff"
"r2_bit": "2^28 + 2^26 + 2^23 - 2^21 + 2^18 - 1"
"znprimroot": 5
- "n": 2147304961
"n_hex": "0x7ffd4601"
"n_bit": "2^31 - 2^18 + 2^16 + 2^14 + 2^11 - 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5 * 93199 + 1"
"nd": 1759069695
"nd_hex": "0x68d945ff"
"nd_bit": "2^31 - 2^29 + 2^27 + 2^24 - 2^21 - 2^19 + 2^16 + 2^14 + 2^11 - 2^9 - 1"
"r2": 1866774515
"r2_hex": "0x6f44b7f3"
"r2_bit": "2^31 - 2^28 - 2^24 + 2^22 + 2^18 + 2^16 - 2^14 - 2^11 - 2^4 + 2^2 - 1"
"znprimroot": 29
- "n": 2147355649
"n_hex": "0x7ffe0c01"
"n_bit": "2^31 - 2^17 + 2^12 - 2^10 + 1"
"n_fac": "2^10 * 3^2 * 41 * 5683 + 1"
"nd": 1869483007
"nd_hex": "0x6f6e0bff"
"nd_bit": "2^31 - 2^28 - 2^23 - 2^20 - 2^17 + 2^12 - 2^10 - 1"
"r2": 1352254458
"r2_hex": "0x5099c3fa"
"r2_bit": "2^30 + 2^28 + 2^23 + 2^21 - 2^19 + 2^17 - 2^14 + 2^10 - 2^3 + 2"
"znprimroot": 11
- "n": 2147281921
"n_hex": "0x7ffcec01"
"n_bit": "2^31 - 2^18 + 2^16 - 2^12 - 2^10 + 1"
"n_fac": "2^10 * 3^3 * 5 * 7^2 * 317 + 1"
"nd": 1181543423
"nd_hex": "0x466cebff"
"nd_bit": "2^30 + 2^27 - 2^25 + 2^23 - 2^20 - 2^18 + 2^16 - 2^12 - 2^10 - 1"
"r2": 2042707951
"r2_hex": "0x79c13fef"
"r2_bit": "2^31 - 2^27 + 2^25 - 2^22 + 2^16 + 2^14 - 2^4 - 1"
"znprimroot": 38
- "n": 2147473409
"n_hex": "0x7fffd801"
"n_bit": "2^31 - 2^13 - 2^11 + 1"
"n_fac": "2^11 * 1048571 + 1"
"nd": 2042615807
"nd_hex": "0x79bfd7ff"
"nd_bit": "2^31 - 2^27 + 2^25 - 2^22 - 2^13 - 2^11 - 1"
"r2": 104837121
"r2_hex": "0x63fb001"
"r2_bit": "2^27 - 2^25 + 2^22 - 2^14 - 2^12 + 1"
"znprimroot": 3
- "n": 2147346433
"n_hex": "0x7ffde801"
"n_bit": "2^31 - 2^17 - 2^13 + 2^11 + 1"
"n_fac": "2^11 * 3^2 * 7 * 11 * 17 * 89 + 1"
"nd": 498984959
"nd_hex": "0x1dbde7ff"
"nd_bit": "2^29 - 2^25 - 2^22 - 2^17 - 2^13 + 2^11 - 1"
"r2": 1649184761
"r2_hex": "0x624c8ff9"
"r2_bit": "2^31 - 2^29 + 2^25 + 2^22 + 2^20 - 2^18 + 2^15 + 2^12 - 2^3 + 1"
"znprimroot": 10
- "n": 2147235841
"n_hex": "0x7ffc3801"
"n_bit": "2^31 - 2^18 + 2^14 - 2^11 + 1"
"n_fac": "2^11 * 3^2 * 5 * 23 * 1013 + 1"
"nd": 867973119
"nd_hex": "0x33bc37ff"
"nd_bit": "2^30 - 2^28 + 2^26 - 2^22 - 2^18 + 2^14 - 2^11 - 1"
"r2": 1285705701
"r2_hex": "0x4ca24fe5"
"r2_bit": "2^30 + 2^28 - 2^26 + 2^23 + 2^21 + 2^17 + 2^14 + 2^12 - 2^5 + 2^2 + 1"
"znprimroot": 17
- "n": 2147389441
"n_hex": "0x7ffe9001"
"n_bit": "2^31 - 2^17 + 2^15 + 2^12 + 1"
"n_fac": "2^12 * 3 * 5 * 7 * 4993 + 1"
"nd": 1862176767
"nd_hex": "0x6efe8fff"
"nd_bit": "2^31 - 2^28 - 2^24 - 2^17 + 2^15 + 2^12 - 1"
"r2": 285401085
"r2_hex": "0x1102dffd"
"r2_bit": "2^28 + 2^24 + 2^18 - 2^16 - 2^13 - 2^2 + 1"
"znprimroot": 11
- "n": 2147217409
"n_hex": "0x7ffbf001"
"n_bit": "2^31 - 2^18 - 2^12 + 1"
"n_fac": "2^12 * 3^2 * 7 * 53 * 157 + 1"
"nd": 2130440191
"nd_hex": "0x7efbefff"
"nd_bit": "2^31 - 2^24 - 2^18 - 2^12 - 1"
"r2": 25030624
"r2_hex": "0x17defe0"
"r2_bit": "2^25 - 2^23 - 2^17 - 2^12 - 2^5"
"znprimroot": 22
- "n": 2147377153
"n_hex": "0x7ffe6001"
"n_bit": "2^31 - 2^17 + 2^15 - 2^13 + 1"
"n_fac": "2^13 * 3 * 23 * 29 * 131 + 1"
"nd": 1543397375
"nd_hex": "0x5bfe5fff"
"nd_bit": "2^31 - 2^29 - 2^26 - 2^17 + 2^15 - 2^13 - 1"
"r2": 604299260
"r2_hex": "0x2404dffc"
"r2_bit": "2^29 + 2^26 + 2^18 + 2^16 - 2^13 - 2^2"
"znprimroot": 5
- "n": 2147205121
"n_hex": "0x7ffbc001"
"n_bit": "2^31 - 2^18 - 2^14 + 1"
"n_fac": "2^14 * 3 * 5 * 8737 + 1"
"nd": 1878769663
"nd_hex": "0x6ffbbfff"
"nd_bit": "2^31 - 2^28 - 2^18 - 2^14 - 1"
"r2": 277905373
"r2_hex": "0x10907fdd"
"r2_bit": "2^28 + 2^23 + 2^20 + 2^15 - 2^5 - 2^2 + 1"
"znprimroot": 7
- "n": 2147352577
"n_hex": "0x7ffe0001"
"n_bit": "2^31 - 2^17 + 1"
"n_fac": "2^17 * 3 * 43 * 127 + 1"
"nd": 2147352575
"nd_hex": "0x7ffdffff"
"nd_bit": "2^31 - 2^17 - 1"
"r2": 786425
"r2_hex": "0xbfff9"
"r2_bit": "2^20 - 2^18 - 2^3 + 1"
"znprimroot": 5
- "n": 2146959361
"n_hex": "0x7ff80001"
"n_bit": "2^31 - 2^19 + 1"
"n_fac": "2^19 * 3^2 * 5 * 7 * 13 + 1"
"nd": 2146959359
"nd_hex": "0x7ff7ffff"
"nd_bit": "2^31 - 2^19 - 1"
"r2": 66060161
"r2_hex": "0x3efff81"
"r2_bit": "2^26 - 2^20 - 2^7 + 1"
"znprimroot": 19
- "n": 1651507201
"n_hex": "0x62700001"
"n_bit": "2^31 - 2^29 + 2^25 + 2^23 - 2^20 + 1"
"n_fac": "2^20 * 3^2 * 5^2 * 7 + 1"
"nd": 1651507199
"nd_hex": "0x626fffff"
"nd_bit": "2^31 - 2^29 + 2^25 + 2^23 - 2^20 - 1"
"r2": 908014223
"r2_hex": "0x361f328f"
"r2_bit": "2^30 - 2^27 - 2^25 + 2^21 - 2^16 + 2^14 - 2^12 + 2^9 + 2^7 + 2^4 - 1"
"znprimroot": 19
- "n": 1541406721
"n_hex": "0x5be00001"
"n_bit": "2^31 - 2^29 - 2^26 - 2^21 + 1"
"n_fac": "2^21 * 3 * 5 * 7^2 + 1"
"nd": 1541406719
"nd_hex": "0x5bdfffff"
"nd_bit": "2^31 - 2^29 - 2^26 - 2^21 - 1"
"r2": 1479259692
"r2_hex": "0x582bb62c"
"r2_bit": "2^31 - 2^29 - 2^27 + 2^22 - 2^20 - 2^18 - 2^14 - 2^11 - 2^9 + 2^6 - 2^4 - 2^2"
"znprimroot": 17
- "n": 1415577601
"n_hex": "0x54600001"
"n_bit": "2^30 + 2^28 + 2^26 + 2^23 - 2^21 + 1"
"n_fac": "2^21 * 3^3 * 5^2 + 1"
"nd": 1415577599
"nd_hex": "0x545fffff"
"nd_bit": "2^30 + 2^28 + 2^26 + 2^23 - 2^21 - 1"
"r2": 206682876
"r2_hex": "0xc51bafc"
"r2_bit": "2^28 - 2^26 + 2^22 + 2^20 + 2^17 - 2^14 - 2^10 - 2^8 - 2^2"
"znprimroot": 17
- "n": 1321205761
"n_hex": "0x4ec00001"
"n_bit": "2^30 + 2^28 - 2^24 - 2^22 + 1"
"n_fac": "2^22 * 3^2 * 5 * 7 + 1"
"nd": 1321205759
"nd_hex": "0x4ebfffff"
"nd_bit": "2^30 + 2^28 - 2^24 - 2^22 - 1"
"r2": 540213043
"r2_hex": "0x2032ff33"
"r2_bit": "2^29 + 2^22 - 2^20 + 2^18 - 2^16 - 2^8 + 2^6 - 2^4 + 2^2 - 1"
"znprimroot": 11
- "n": 880803841
"n_hex": "0x34800001"
"n_bit": "2^30 - 2^28 + 2^26 + 2^23 + 1"
"n_fac": "2^23 * 3 * 5 * 7 + 1"
"nd": 880803839
"nd_hex": "0x347fffff"
"nd_bit": "2^30 - 2^28 + 2^26 + 2^23 - 1"
"r2": 116162254
"r2_hex": "0x6ec7ece"
"r2_bit": "2^27 - 2^24 - 2^20 - 2^18 + 2^15 - 2^8 - 2^6 + 2^4 - 2"
"znprimroot": 26
- "n": 2130706433
"n_hex": "0x7f000001"
"n_bit": "2^31 - 2^24 + 1"
"n_fac": "2^24 * 127 + 1"
"nd": 2130706431
"nd_hex": "0x7effffff"
"nd_bit": "2^31 - 2^24 - 1"
"r2": 100531193
"r2_hex": "0x5fdfbf9"
"r2_bit": "2^27 - 2^25 - 2^17 - 2^10 - 2^3 + 1"
"znprimroot": 3
- "n": 754974721
"n_hex": "0x2d000001"
"n_bit": "2^30 - 2^28 - 2^26 + 2^24 + 1"
"n_fac": "2^24 * 3^2 * 5 + 1"
"nd": 754974719
"nd_hex": "0x2cffffff"
"nd_bit": "2^30 - 2^28 - 2^26 + 2^24 - 1"
"r2": 753483421
"r2_hex": "0x2ce93e9d"
"r2_bit": "2^30 - 2^28 - 2^26 + 2^24 - 2^21 + 2^19 + 2^16 + 2^14 - 2^9 + 2^7 + 2^5 - 2^2 + 1"
"znprimroot": 11
- "n": 2113929217
"n_hex": "0x7e000001"
"n_bit": "2^31 - 2^25 + 1"
"n_fac": "2^25 * 3^2 * 7 + 1"
"nd": 2113929215
"nd_hex": "0x7dffffff"
"nd_bit": "2^31 - 2^25 - 1"
"r2": 2113396608
"r2_hex": "0x7df7df80"
"r2_bit": "2^31 - 2^25 - 2^19 - 2^13 - 2^7"
"znprimroot": 5
- "n": 1811939329
"n_hex": "0x6c000001"
"n_bit": "2^31 - 2^28 - 2^26 + 1"
"n_fac": "2^26 * 3^3 + 1"
"nd": 1811939327
"nd_hex": "0x6bffffff"
"nd_bit": "2^31 - 2^28 - 2^26 - 1"
"r2": 1145821717
"r2_hex": "0x444bda15"
"r2_bit": "2^30 + 2^26 + 2^22 + 2^20 - 2^18 - 2^13 - 2^11 + 2^9 + 2^4 + 2^2 + 1"
"znprimroot": 13
- "n": 2013265921
"n_hex": "0x78000001"
"n_bit": "2^31 - 2^27 + 1"
"n_fac": "2^27 * 3 * 5 + 1"
"nd": 2013265919
"nd_hex": "0x77ffffff"
"nd_bit": "2^31 - 2^27 - 1"
"r2": 796358521
"r2_hex": "0x2f777779"
"r2_bit": "2^30 - 2^28 - 2^23 - 2^19 - 2^15 - 2^11 - 2^7 - 2^3 + 1"
"znprimroot": 31
Raw
result_prime_0032.yaml
- "r": 32
"primes":
- "n": 4294967291
"n_hex": "0xfffffffb"
"n_bit": "2^32 - 2^2 - 1"
"n_fac": "2 * 5 * 19 * 22605091 + 1"
"nd": 3435973837
"nd_hex": "0xcccccccd"
"nd_bit": "2^32 - 2^30 + 2^28 - 2^26 + 2^24 - 2^22 + 2^20 - 2^18 + 2^16 - 2^14 + 2^12 - 2^10 + 2^8 - 2^6 + 2^4 - 2^2 + 1"
"r2": 25
"r2_hex": "0x19"
"r2_bit": "2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 4294966591
"n_hex": "0xfffffd3f"
"n_bit": "2^32 - 2^10 + 2^8 + 2^6 - 1"
"n_fac": "2 * 3^2 * 5 * 47721851 + 1"
"nd": 1547406657
"nd_hex": "0x5c3b8d41"
"nd_bit": "2^31 - 2^29 - 2^26 + 2^22 - 2^18 - 2^15 + 2^12 - 2^10 + 2^8 + 2^6 + 1"
"r2": 497025
"r2_hex": "0x79581"
"r2_bit": "2^19 - 2^15 + 2^13 - 2^11 - 2^9 - 2^7 + 1"
"znprimroot": 3
- "n": 4294965151
"n_hex": "0xfffff79f"
"n_bit": "2^32 - 2^11 - 2^7 + 2^5 - 1"
"n_fac": "2 * 3^2 * 5^2 * 7^2 * 109 * 1787 + 1"
"nd": 1139317665
"nd_hex": "0x43e89ba1"
"nd_bit": "2^30 + 2^26 - 2^21 + 2^19 + 2^15 + 2^13 - 2^10 - 2^7 + 2^5 + 1"
"r2": 4601025
"r2_hex": "0x4634c1"
"r2_bit": "2^22 + 2^19 - 2^17 + 2^14 - 2^12 + 2^10 + 2^8 - 2^6 + 1"
"znprimroot": 6
- "n": 4294967197
"n_hex": "0xffffff9d"
"n_bit": "2^32 - 2^7 + 2^5 - 2^2 + 1"
"n_fac": "2^2 * 3 * 13 * 67 * 163 * 2521 + 1"
"nd": 3210379595
"nd_hex": "0xbf5a814b"
"nd_bit": "2^32 - 2^30 - 2^23 - 2^21 - 2^19 + 2^17 + 2^15 + 2^8 + 2^6 + 2^4 - 2^2 - 1"
"r2": 9801
"r2_hex": "0x2649"
"r2_bit": "2^13 + 2^11 - 2^9 + 2^6 + 2^3 + 1"
"znprimroot": 6
- "n": 4294967161
"n_hex": "0xffffff79"
"n_bit": "2^32 - 2^7 - 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 11 * 47 * 107 * 647 + 1"
"nd": 3785934135
"nd_hex": "0xe1a8c537"
"nd_bit": "2^32 - 2^29 + 2^25 - 2^23 + 2^21 + 2^19 + 2^16 - 2^14 + 2^10 + 2^8 + 2^6 - 2^3 - 1"
"r2": 18225
"r2_hex": "0x4731"
"r2_bit": "2^14 + 2^11 - 2^8 + 2^6 - 2^4 + 1"
"znprimroot": 58
- "n": 4294964521
"n_hex": "0xfffff529"
"n_bit": "2^32 - 2^12 + 2^10 + 2^8 + 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^3 * 5 * 7 * 11 * 51647 + 1"
"nd": 1693223143
"nd_hex": "0x64ec88e7"
"nd_bit": "2^31 - 2^29 + 2^26 + 2^24 - 2^20 - 2^18 + 2^15 + 2^11 + 2^8 - 2^5 + 2^3 - 1"
"r2": 7700625
"r2_hex": "0x758091"
"r2_bit": "2^23 - 2^19 - 2^17 - 2^15 + 2^7 + 2^4 + 1"
"znprimroot": 17
- "n": 4294966769
"n_hex": "0xfffffdf1"
"n_bit": "2^32 - 2^9 - 2^4 + 1"
"n_fac": "2^4 * 17 * 569 * 27751 + 1"
"nd": 2208607471
"nd_hex": "0x83a4acef"
"nd_bit": "2^31 + 2^26 - 2^23 + 2^21 + 2^18 + 2^16 - 2^14 - 2^12 - 2^10 + 2^8 - 2^4 - 1"
"r2": 277729
"r2_hex": "0x43ce1"
"r2_bit": "2^18 + 2^14 - 2^10 + 2^8 - 2^5 + 1"
"znprimroot": 3
- "n": 4294965841
"n_hex": "0xfffffa51"
"n_bit": "2^32 - 2^11 + 2^9 + 2^6 + 2^4 + 1"
"n_fac": "2^4 * 3 * 5 * 11 * 1626881 + 1"
"nd": 4114903375
"nd_hex": "0xf544714f"
"nd_bit": "2^32 - 2^28 + 2^26 + 2^24 + 2^22 + 2^18 + 2^15 - 2^12 + 2^8 + 2^6 + 2^4 - 1"
"r2": 2117025
"r2_hex": "0x204da1"
"r2_bit": "2^21 + 2^14 + 2^12 - 2^9 - 2^7 + 2^5 + 1"
"znprimroot": 7
- "n": 4294965361
"n_hex": "0xfffff871"
"n_bit": "2^32 - 2^11 + 2^7 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5 * 7 * 1093 * 2339 + 1"
"nd": 1163081583
"nd_hex": "0x4553376f"
"nd_bit": "2^30 + 2^26 + 2^24 + 2^22 + 2^20 + 2^18 - 2^16 + 2^14 - 2^11 - 2^7 - 2^4 - 1"
"r2": 3744225
"r2_hex": "0x3921e1"
"r2_bit": "2^22 - 2^19 + 2^16 + 2^13 + 2^9 - 2^5 + 1"
"znprimroot": 13
- "n": 4294966177
"n_hex": "0xfffffba1"
"n_bit": "2^32 - 2^10 - 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 31 * 481067 + 1"
"nd": 3911145375
"nd_hex": "0xe91f579f"
"nd_bit": "2^32 - 2^29 + 2^27 + 2^24 + 2^21 - 2^15 - 2^13 - 2^11 - 2^7 + 2^5 - 1"
"r2": 1252161
"r2_hex": "0x131b41"
"r2_bit": "2^20 + 2^18 - 2^16 + 2^13 - 2^10 - 2^8 + 2^6 + 1"
"znprimroot": 5
- "n": 4294965601
"n_hex": "0xfffff961"
"n_bit": "2^32 - 2^11 + 2^9 - 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5^2 * 198841 + 1"
"nd": 4026373471
"nd_hex": "0xeffd955f"
"nd_bit": "2^32 - 2^28 - 2^17 - 2^15 + 2^13 - 2^11 - 2^9 - 2^7 - 2^5 - 1"
"r2": 2873025
"r2_hex": "0x2bd6c1"
"r2_bit": "2^22 - 2^20 - 2^18 - 2^13 - 2^11 - 2^8 - 2^6 + 1"
"znprimroot": 7
- "n": 4294963681
"n_hex": "0xfffff1e1"
"n_bit": "2^32 - 2^12 + 2^9 - 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 7^3 * 19 * 1373 + 1"
"nd": 3741314527
"nd_hex": "0xdeffeddf"
"nd_bit": "2^32 - 2^29 - 2^24 - 2^12 - 2^9 - 2^5 - 1"
"r2": 13068225
"r2_hex": "0xc767c1"
"r2_bit": "2^24 - 2^22 + 2^19 - 2^15 - 2^13 + 2^11 - 2^6 + 1"
"znprimroot": 44
- "n": 4294965313
"n_hex": "0xfffff841"
"n_bit": "2^32 - 2^11 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 11 * 701 * 967 + 1"
"nd": 3980912703
"nd_hex": "0xed47e83f"
"nd_bit": "2^32 - 2^28 - 2^26 + 2^24 + 2^22 + 2^19 - 2^13 + 2^11 + 2^6 - 1"
"r2": 3932289
"r2_hex": "0x3c0081"
"r2_bit": "2^22 - 2^18 + 2^7 + 1"
"znprimroot": 5
- "n": 4294960321
"n_hex": "0xffffe4c1"
"n_bit": "2^32 - 2^13 + 2^10 + 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 7 * 29 * 22039 + 1"
"nd": 2705675455
"nd_hex": "0xa14554bf"
"nd_bit": "2^31 + 2^29 + 2^24 + 2^22 + 2^18 + 2^16 + 2^14 + 2^12 + 2^10 + 2^8 - 2^6 - 1"
"r2": 48650625
"r2_hex": "0x2e65981"
"r2_bit": "2^26 - 2^24 - 2^21 + 2^19 - 2^17 + 2^15 - 2^13 - 2^11 + 2^9 - 2^7 + 1"
"znprimroot": 13
- "n": 4294958401
"n_hex": "0xffffdd41"
"n_bit": "2^32 - 2^13 - 2^10 + 2^8 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5^2 * 298261 + 1"
"nd": 528239935
"nd_hex": "0x1f7c4d3f"
"nd_bit": "2^29 - 2^23 - 2^18 + 2^14 + 2^12 - 2^10 + 2^8 + 2^6 - 1"
"r2": 79121025
"r2_hex": "0x4b74a81"
"r2_bit": "2^26 + 2^24 - 2^22 - 2^19 - 2^16 + 2^14 + 2^11 + 2^9 + 2^7 + 1"
"znprimroot": 13
- "n": 4294946881
"n_hex": "0xffffb041"
"n_bit": "2^32 - 2^14 - 2^12 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 7 * 213043 + 1"
"nd": 3609960511
"nd_hex": "0xd72ba03f"
"nd_bit": "2^32 - 2^29 - 2^27 - 2^24 + 2^22 - 2^20 - 2^18 - 2^15 + 2^13 + 2^6 - 1"
"r2": 416772225
"r2_hex": "0x18d77081"
"r2_bit": "2^29 - 2^27 + 2^24 - 2^21 - 2^19 - 2^15 - 2^12 + 2^7 + 1"
"znprimroot": 17
- "n": 4294966657
"n_hex": "0xfffffd81"
"n_bit": "2^32 - 2^9 - 2^7 + 1"
"n_fac": "2^7 * 3 * 641 * 17449 + 1"
"nd": 3763977599
"nd_hex": "0xe059bd7f"
"nd_bit": "2^32 - 2^29 + 2^23 - 2^21 - 2^19 + 2^17 - 2^14 - 2^9 - 2^7 - 1"
"r2": 408321
"r2_hex": "0x63b01"
"r2_bit": "2^19 - 2^17 + 2^14 - 2^10 - 2^8 + 1"
"znprimroot": 5
- "n": 4294953601
"n_hex": "0xffffca81"
"n_bit": "2^32 - 2^14 + 2^11 + 2^9 + 2^7 + 1"
"n_fac": "2^7 * 3 * 5^2 * 7 * 63913 + 1"
"nd": 3128003199
"nd_hex": "0xba718a7f"
"nd_bit": "2^32 - 2^30 - 2^27 + 2^25 + 2^23 - 2^20 + 2^17 - 2^15 + 2^11 + 2^9 + 2^7 - 1"
"r2": 187553025
"r2_hex": "0xb2dd501"
"r2_bit": "2^28 - 2^26 - 2^24 + 2^22 - 2^20 - 2^17 - 2^14 + 2^12 + 2^10 + 2^8 + 1"
"znprimroot": 37
- "n": 4294800001
"n_hex": "0xfffd7281"
"n_bit": "2^32 - 2^17 - 2^15 - 2^12 + 2^9 + 2^7 + 1"
"n_fac": "2^7 * 3^2 * 5^5 * 1193 + 1"
"nd": 4016517759
"nd_hex": "0xef67327f"
"nd_bit": "2^32 - 2^28 - 2^23 - 2^21 + 2^19 - 2^16 + 2^14 - 2^12 + 2^9 + 2^7 - 1"
"r2": 2218817019
"r2_hex": "0x844075fb"
"r2_bit": "2^31 + 2^26 + 2^22 + 2^15 - 2^11 - 2^9 - 2^2 - 1"
"znprimroot": 11
- "n": 4294604161
"n_hex": "0xfffa7581"
"n_bit": "2^32 - 2^19 + 2^17 + 2^15 - 2^11 - 2^9 - 2^7 + 1"
"n_fac": "2^7 * 3^2 * 5 * 7 * 11 * 23 * 421 + 1"
"nd": 2523673983
"nd_hex": "0x966c357f"
"nd_bit": "2^31 + 2^29 - 2^27 - 2^25 + 2^23 - 2^20 - 2^18 + 2^14 - 2^11 - 2^9 - 2^7 - 1"
"r2": 3028903395
"r2_hex": "0xb48965e3"
"r2_bit": "2^32 - 2^30 - 2^28 + 2^26 + 2^23 + 2^19 + 2^17 - 2^15 - 2^13 + 2^11 - 2^9 - 2^5 + 2^2 - 1"
"znprimroot": 29
- "n": 4294953217
"n_hex": "0xffffc901"
"n_bit": "2^32 - 2^14 + 2^11 + 2^8 + 1"
"n_fac": "2^8 * 3^2 * 139 * 13411 + 1"
"nd": 221169919
"nd_hex": "0xd2ec8ff"
"nd_bit": "2^28 - 2^26 + 2^24 + 2^22 - 2^20 - 2^16 - 2^14 + 2^11 + 2^8 - 1"
"r2": 198218241
"r2_hex": "0xbd09201"
"r2_bit": "2^28 - 2^26 - 2^22 + 2^20 + 2^15 + 2^12 + 2^9 + 1"
"znprimroot": 5
- "n": 4294928641
"n_hex": "0xffff6901"
"n_bit": "2^32 - 2^15 - 2^13 + 2^11 + 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 107 * 10453 + 1"
"nd": 2683201791
"nd_hex": "0x9fee68ff"
"nd_bit": "2^31 + 2^29 - 2^20 - 2^17 + 2^15 - 2^13 + 2^11 + 2^8 - 1"
"r2": 1494209025
"r2_hex": "0x590fd201"
"r2_bit": "2^31 - 2^29 - 2^27 + 2^24 + 2^20 - 2^14 + 2^12 + 2^9 + 1"
"znprimroot": 21
- "n": 4294913281
"n_hex": "0xffff2d01"
"n_bit": "2^32 - 2^16 + 2^14 - 2^12 - 2^10 + 2^8 + 1"
"n_fac": "2^8 * 3 * 5 * 7 * 23 * 6947 + 1"
"nd": 1192635647
"nd_hex": "0x47162cff"
"nd_bit": "2^30 + 2^27 - 2^24 + 2^21 - 2^19 - 2^17 + 2^14 - 2^12 - 2^10 + 2^8 - 1"
"r2": 2917620225
"r2_hex": "0xade75a01"
"r2_bit": "2^32 - 2^30 - 2^28 - 2^25 - 2^21 + 2^19 - 2^15 - 2^13 - 2^11 + 2^9 + 1"
"znprimroot": 11
- "n": 4294321921
"n_hex": "0xfff62701"
"n_bit": "2^32 - 2^19 - 2^17 + 2^13 + 2^11 - 2^8 + 1"
"n_fac": "2^8 * 3^4 * 5 * 7 * 61 * 97 + 1"
"nd": 3171231487
"nd_hex": "0xbd0526ff"
"nd_bit": "2^32 - 2^30 - 2^26 + 2^24 + 2^18 + 2^16 + 2^13 + 2^11 - 2^8 - 1"
"r2": 4253986209
"r2_hex": "0xfd8eada1"
"r2_bit": "2^32 - 2^25 - 2^23 + 2^20 - 2^16 - 2^14 - 2^12 - 2^9 - 2^7 + 2^5 + 1"
"znprimroot": 13
- "n": 4294962689
"n_hex": "0xffffee01"
"n_bit": "2^32 - 2^12 - 2^9 + 1"
"n_fac": "2^9 * 17 * 493447 + 1"
"nd": 918285823
"nd_hex": "0x36bbedff"
"nd_bit": "2^30 - 2^27 - 2^24 - 2^22 - 2^18 - 2^12 - 2^9 - 1"
"r2": 21224449
"r2_hex": "0x143dc01"
"r2_bit": "2^24 + 2^22 + 2^18 - 2^13 - 2^10 + 1"
"znprimroot": 3
- "n": 4294937089
"n_hex": "0xffff8a01"
"n_bit": "2^32 - 2^15 + 2^11 + 2^9 + 1"
"n_fac": "2^9 * 3^3 * 13 * 23899 + 1"
"nd": 2979760639
"nd_hex": "0xb19b89ff"
"nd_bit": "2^32 - 2^30 - 2^28 + 2^25 - 2^23 + 2^21 - 2^18 - 2^15 + 2^11 + 2^9 - 1"
"r2": 912462849
"r2_hex": "0x36631401"
"r2_bit": "2^30 - 2^27 - 2^25 + 2^23 - 2^21 + 2^18 - 2^16 + 2^12 + 2^10 + 1"
"znprimroot": 17
- "n": 4294510081
"n_hex": "0xfff90601"
"n_bit": "2^32 - 2^19 + 2^16 + 2^11 - 2^9 + 1"
"n_fac": "2^9 * 3 * 5 * 7 * 17 * 37 * 127 + 1"
"nd": 735380991
"nd_hex": "0x2bd505ff"
"nd_bit": "2^30 - 2^28 - 2^26 - 2^22 + 2^20 + 2^18 + 2^16 + 2^11 - 2^9 - 1"
"r2": 2909072337
"r2_hex": "0xad64ebd1"
"r2_bit": "2^32 - 2^30 - 2^28 - 2^25 - 2^23 - 2^21 + 2^18 + 2^16 - 2^12 - 2^10 - 2^6 + 2^4 + 1"
"znprimroot": 29
- "n": 4294080001
"n_hex": "0xfff27601"
"n_bit": "2^32 - 2^20 + 2^17 + 2^15 - 2^11 - 2^9 + 1"
"n_fac": "2^9 * 3^3 * 5^4 * 7 * 71 + 1"
"nd": 3381556735
"nd_hex": "0xc98e75ff"
"nd_bit": "2^32 - 2^30 + 2^27 + 2^25 - 2^23 + 2^20 - 2^17 + 2^15 - 2^11 - 2^9 - 1"
"r2": 1475776842
"r2_hex": "0x57f6914a"
"r2_bit": "2^31 - 2^29 - 2^27 - 2^19 - 2^17 + 2^15 + 2^12 + 2^8 + 2^6 + 2^3 + 2"
"znprimroot": 23
- "n": 4294702081
"n_hex": "0xfffbf401"
"n_bit": "2^32 - 2^18 - 2^12 + 2^10 + 1"
"n_fac": "2^10 * 3^3 * 5 * 47 * 661 + 1"
"nd": 3748393983
"nd_hex": "0xdf6bf3ff"
"nd_bit": "2^32 - 2^29 - 2^23 - 2^20 - 2^18 - 2^12 + 2^10 - 1"
"r2": 1623762929
"r2_hex": "0x60c8a7f1"
"r2_bit": "2^31 - 2^29 + 2^24 - 2^22 + 2^19 + 2^15 + 2^13 + 2^11 - 2^4 + 1"
"znprimroot": 7
- "n": 4294957057
"n_hex": "0xffffd801"
"n_bit": "2^32 - 2^13 - 2^11 + 1"
"n_fac": "2^11 * 3 * 13 * 53773 + 1"
"nd": 4190099455
"nd_hex": "0xf9bfd7ff"
"nd_bit": "2^32 - 2^27 + 2^25 - 2^22 - 2^13 - 2^11 - 1"
"r2": 104837121
"r2_hex": "0x63fb001"
"r2_bit": "2^27 - 2^25 + 2^22 - 2^14 - 2^12 + 1"
"znprimroot": 10
- "n": 4294809601
"n_hex": "0xfffd9801"
"n_bit": "2^32 - 2^17 - 2^15 + 2^13 - 2^11 + 1"
"n_fac": "2^11 * 3 * 5^2 * 27961 + 1"
"nd": 901617663
"nd_hex": "0x35bd97ff"
"nd_bit": "2^30 - 2^27 - 2^25 - 2^22 - 2^17 - 2^15 + 2^13 - 2^11 - 1"
"r2": 3393665020
"r2_hex": "0xca4737fc"
"r2_bit": "2^32 - 2^30 + 2^27 + 2^25 + 2^22 + 2^19 - 2^16 + 2^14 - 2^11 - 2^2"
"znprimroot": 14
- "n": 4294133761
"n_hex": "0xfff34801"
"n_bit": "2^32 - 2^20 + 2^18 - 2^16 + 2^14 + 2^11 + 1"
"n_fac": "2^11 * 3 * 5 * 7 * 19 * 1051 + 1"
"nd": 1001605119
"nd_hex": "0x3bb347ff"
"nd_bit": "2^30 - 2^26 - 2^22 - 2^20 + 2^18 - 2^16 + 2^14 + 2^11 - 1"
"r2": 3425060704
"r2_hex": "0xcc264760"
"r2_bit": "2^32 - 2^30 + 2^28 - 2^26 + 2^21 + 2^19 - 2^17 + 2^14 + 2^11 - 2^7 - 2^5"
"znprimroot": 17
- "n": 4294955009
"n_hex": "0xffffd001"
"n_bit": "2^32 - 2^14 + 2^12 + 1"
"n_fac": "2^12 * 1048573 + 1"
"nd": 4143960063
"nd_hex": "0xf6ffcfff"
"nd_bit": "2^32 - 2^27 - 2^24 - 2^14 + 2^12 - 1"
"r2": 150970369
"r2_hex": "0x8ffa001"
"r2_bit": "2^27 + 2^24 - 2^15 + 2^13 + 1"
"znprimroot": 3
- "n": 4294914049
"n_hex": "0xffff3001"
"n_bit": "2^32 - 2^16 + 2^14 - 2^12 + 1"
"n_fac": "2^12 * 3^2 * 116507 + 1"
"nd": 1459564543
"nd_hex": "0x56ff2fff"
"nd_bit": "2^31 - 2^29 - 2^27 - 2^24 - 2^16 + 2^14 - 2^12 - 1"
"r2": 2835243009
"r2_hex": "0xa8fe6001"
"r2_bit": "2^31 + 2^29 + 2^27 + 2^24 - 2^17 + 2^15 - 2^13 + 1"
"znprimroot": 7
- "n": 4294103041
"n_hex": "0xfff2d001"
"n_bit": "2^32 - 2^20 + 2^18 - 2^16 - 2^14 + 2^12 + 1"
"n_fac": "2^12 * 3^2 * 5 * 23297 + 1"
"nd": 385011711
"nd_hex": "0x16f2cfff"
"nd_bit": "2^29 - 2^27 - 2^24 - 2^20 + 2^18 - 2^16 - 2^14 + 2^12 - 1"
"r2": 4056878932
"r2_hex": "0xf1cf0f54"
"r2_bit": "2^32 - 2^28 + 2^25 - 2^22 + 2^20 - 2^16 + 2^12 - 2^8 + 2^6 + 2^4 + 2^2"
"znprimroot": 23
- "n": 4294828033
"n_hex": "0xfffde001"
"n_bit": "2^32 - 2^17 - 2^13 + 1"
"n_fac": "2^13 * 3 * 11 * 15887 + 1"
"nd": 2080235519
"nd_hex": "0x7bfddfff"
"nd_bit": "2^31 - 2^26 - 2^17 - 2^13 - 1"
"r2": 2214871037
"r2_hex": "0x84043ffd"
"r2_bit": "2^31 + 2^26 + 2^18 + 2^14 - 2^2 + 1"
"znprimroot": 10
- "n": 4294729729
"n_hex": "0xfffc6001"
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"n_fac": "2^13 * 3^3 * 19417 + 1"
"nd": 3690749951
"nd_hex": "0xdbfc5fff"
"nd_bit": "2^32 - 2^29 - 2^26 - 2^18 + 2^15 - 2^13 - 1"
"r2": 606593012
"r2_hex": "0x2427dff4"
"r2_bit": "2^29 + 2^26 + 2^21 + 2^19 - 2^13 - 2^4 + 2^2"
"znprimroot": 21
- "n": 4294475777
"n_hex": "0xfff88001"
"n_bit": "2^32 - 2^19 + 2^15 + 1"
"n_fac": "2^15 * 83 * 1579 + 1"
"nd": 3220733951
"nd_hex": "0xbff87fff"
"nd_bit": "2^32 - 2^30 - 2^19 + 2^15 - 1"
"r2": 1100283849
"r2_hex": "0x4194ffc9"
"r2_bit": "2^30 + 2^25 - 2^23 + 2^20 + 2^18 + 2^16 - 2^6 + 2^3 + 1"
"znprimroot": 5
- "n": 4293918721
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"n_bit": "2^32 - 2^20 + 1"
"n_fac": "2^20 * 3^2 * 5 * 7 * 13 + 1"
"nd": 4293918719
"nd_hex": "0xffefffff"
"nd_bit": "2^32 - 2^20 - 1"
"r2": 266338049
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"r2_bit": "2^28 - 2^21 - 2^8 + 1"
"znprimroot": 19
- "n": 4276092929
"n_hex": "0xfee00001"
"n_bit": "2^32 - 2^24 - 2^21 + 1"
"n_fac": "2^21 * 2039 + 1"
"nd": 4276092927
"nd_hex": "0xfedfffff"
"nd_bit": "2^32 - 2^24 - 2^21 - 1"
"r2": 427735699
"r2_hex": "0x197eba93"
"r2_bit": "2^29 - 2^27 + 2^25 - 2^23 - 2^16 - 2^14 - 2^11 + 2^9 + 2^7 + 2^4 + 2^2 - 1"
"znprimroot": 3
- "n": 4183818241
"n_hex": "0xf9600001"
"n_bit": "2^32 - 2^27 + 2^25 - 2^23 - 2^21 + 1"
"n_fac": "2^21 * 3 * 5 * 7 * 19 + 1"
"nd": 4183818239
"nd_hex": "0xf95fffff"
"nd_bit": "2^32 - 2^27 + 2^25 - 2^23 - 2^21 - 1"
"r2": 43184513
"r2_hex": "0x292f181"
"r2_bit": "2^25 + 2^23 + 2^20 + 2^18 - 2^16 - 2^12 + 2^9 - 2^7 + 1"
"znprimroot": 13
- "n": 3837788161
"n_hex": "0xe4c00001"
"n_bit": "2^32 - 2^29 + 2^26 + 2^24 - 2^22 + 1"
"n_fac": "2^22 * 3 * 5 * 61 + 1"
"nd": 3837788159
"nd_hex": "0xe4bfffff"
"nd_bit": "2^32 - 2^29 + 2^26 + 2^24 - 2^22 - 1"
"r2": 2319514289
"r2_hex": "0x8a40fab1"
"r2_bit": "2^31 + 2^27 + 2^25 + 2^22 + 2^16 - 2^10 - 2^8 - 2^6 - 2^4 + 1"
"znprimroot": 31
- "n": 3208642561
"n_hex": "0xbf400001"
"n_bit": "2^32 - 2^30 - 2^24 + 2^22 + 1"
"n_fac": "2^22 * 3^2 * 5 * 17 + 1"
"nd": 3208642559
"nd_hex": "0xbf3fffff"
"nd_bit": "2^32 - 2^30 - 2^24 + 2^22 - 1"
"r2": 2824076972
"r2_hex": "0xa853feac"
"r2_bit": "2^31 + 2^29 + 2^27 + 2^22 + 2^20 + 2^18 - 2^8 - 2^6 - 2^4 - 2^2"
"znprimroot": 13
- "n": 1321205761
"n_hex": "0x4ec00001"
"n_bit": "2^30 + 2^28 - 2^24 - 2^22 + 1"
"n_fac": "2^22 * 3^2 * 5 * 7 + 1"
"nd": 1321205759
"nd_hex": "0x4ebfffff"
"nd_bit": "2^30 + 2^28 - 2^24 - 2^22 - 1"
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"r2_bit": "2^30 - 2^28 + 2^25 + 2^20 - 2^18 - 2^10 + 2^8 - 2^6 + 2^4 - 2^2 - 1"
"znprimroot": 11
- "n": 4253024257
"n_hex": "0xfd800001"
"n_bit": "2^32 - 2^25 - 2^23 + 1"
"n_fac": "2^23 * 3 * 13^2 + 1"
"nd": 4253024255
"nd_hex": "0xfd7fffff"
"nd_bit": "2^32 - 2^25 - 2^23 - 1"
"r2": 1819914298
"r2_hex": "0x6c79b03a"
"r2_bit": "2^31 - 2^28 - 2^26 + 2^23 - 2^19 + 2^17 - 2^14 - 2^12 + 2^6 - 2^3 + 2"
"znprimroot": 5
- "n": 880803841
"n_hex": "0x34800001"
"n_bit": "2^30 - 2^28 + 2^26 + 2^23 + 1"
"n_fac": "2^23 * 3 * 5 * 7 + 1"
"nd": 880803839
"nd_hex": "0x347fffff"
"nd_bit": "2^30 - 2^28 + 2^26 + 2^23 - 1"
"r2": 464649016
"r2_hex": "0x1bb1fb38"
"r2_bit": "2^29 - 2^26 - 2^22 - 2^20 + 2^17 - 2^10 - 2^8 + 2^6 - 2^3"
"znprimroot": 26
- "n": 4076863489
"n_hex": "0xf3000001"
"n_bit": "2^32 - 2^28 + 2^26 - 2^24 + 1"
"n_fac": "2^24 * 3^5 + 1"
"nd": 4076863487
"nd_hex": "0xf2ffffff"
"nd_bit": "2^32 - 2^28 + 2^26 - 2^24 - 1"
"r2": 3444438393
"r2_hex": "0xcd4df579"
"r2_bit": "2^32 - 2^30 + 2^28 - 2^26 + 2^24 + 2^22 + 2^20 - 2^17 - 2^11 - 2^9 - 2^7 - 2^3 + 1"
"znprimroot": 7
- "n": 754974721
"n_hex": "0x2d000001"
"n_bit": "2^30 - 2^28 - 2^26 + 2^24 + 1"
"n_fac": "2^24 * 3^2 * 5 + 1"
"nd": 754974719
"nd_hex": "0x2cffffff"
"nd_bit": "2^30 - 2^28 - 2^26 + 2^24 - 1"
"r2": 749009521
"r2_hex": "0x2ca4fa71"
"r2_bit": "2^30 - 2^28 - 2^26 + 2^23 + 2^21 + 2^18 + 2^16 - 2^11 + 2^9 + 2^7 - 2^4 + 1"
"znprimroot": 11
- "n": 4194304001
"n_hex": "0xfa000001"
"n_bit": "2^32 - 2^27 + 2^25 + 1"
"n_fac": "2^25 * 5^3 + 1"
"nd": 4194303999
"nd_hex": "0xf9ffffff"
"nd_bit": "2^32 - 2^27 + 2^25 - 1"
"r2": 232465106
"r2_hex": "0xddb22d2"
"r2_bit": "2^28 - 2^25 - 2^21 - 2^18 - 2^16 + 2^13 + 2^10 - 2^8 - 2^6 + 2^4 + 2"
"znprimroot": 3
- "n": 2717908993
"n_hex": "0xa2000001"
"n_bit": "2^31 + 2^29 + 2^25 + 1"
"n_fac": "2^25 * 3^4 + 1"
"nd": 2717908991
"nd_hex": "0xa1ffffff"
"nd_bit": "2^31 + 2^29 + 2^25 - 1"
"r2": 2541023286
"r2_hex": "0x9774f036"
"r2_bit": "2^31 + 2^29 - 2^27 - 2^23 - 2^20 + 2^18 + 2^16 - 2^12 + 2^6 - 2^3 - 2"
"znprimroot": 5
- "n": 1811939329
"n_hex": "0x6c000001"
"n_bit": "2^31 - 2^28 - 2^26 + 1"
"n_fac": "2^26 * 3^3 + 1"
"nd": 1811939327
"nd_hex": "0x6bffffff"
"nd_bit": "2^31 - 2^28 - 2^26 - 1"
"r2": 959408210
"r2_hex": "0x392f6852"
"r2_bit": "2^30 - 2^27 + 2^24 + 2^22 - 2^20 - 2^15 - 2^13 + 2^11 + 2^6 + 2^4 + 2"
"znprimroot": 13
- "n": 3892314113
"n_hex": "0xe8000001"
"n_bit": "2^32 - 2^29 + 2^27 + 1"
"n_fac": "2^27 * 29 + 1"
"nd": 3892314111
"nd_hex": "0xe7ffffff"
"nd_bit": "2^32 - 2^29 + 2^27 - 1"
"r2": 1703176688
"r2_hex": "0x658469f0"
"r2_bit": "2^31 - 2^29 + 2^27 - 2^25 - 2^23 + 2^18 + 2^15 - 2^13 + 2^11 + 2^9 - 2^4"
"znprimroot": 3
- "n": 2013265921
"n_hex": "0x78000001"
"n_bit": "2^31 - 2^27 + 1"
"n_fac": "2^27 * 3 * 5 + 1"
"nd": 2013265919
"nd_hex": "0x77ffffff"
"nd_bit": "2^31 - 2^27 - 1"
"r2": 1172168163
"r2_hex": "0x45dddde3"
"r2_bit": "2^30 + 2^27 - 2^25 - 2^21 - 2^17 - 2^13 - 2^9 - 2^5 + 2^2 - 1"
"znprimroot": 31
- "n": 3489660929
"n_hex": "0xd0000001"
"n_bit": "2^32 - 2^30 + 2^28 + 1"
"n_fac": "2^28 * 13 + 1"
"nd": 3489660927
"nd_hex": "0xcfffffff"
"nd_bit": "2^32 - 2^30 + 2^28 - 1"
"r2": 1961643719
"r2_hex": "0x74ec4ec7"
"r2_bit": "2^31 - 2^28 + 2^26 + 2^24 - 2^20 - 2^18 + 2^14 + 2^12 - 2^8 - 2^6 + 2^3 - 1"
"znprimroot": 3
- "n": 3221225473
"n_hex": "0xc0000001"
"n_bit": "2^32 - 2^30 + 1"
"n_fac": "2^30 * 3 + 1"
"nd": 3221225471
"nd_hex": "0xbfffffff"
"nd_bit": "2^32 - 2^30 - 1"
"r2": 1789569709
"r2_hex": "0x6aaaaaad"
"r2_bit": "2^31 - 2^28 - 2^26 - 2^24 - 2^22 - 2^20 - 2^18 - 2^16 - 2^14 - 2^12 - 2^10 - 2^8 - 2^6 - 2^4 - 2^2 + 1"
"znprimroot": 5
Raw
result_prime_0046.yaml
- "r": 46
"primes":
- "n": 70368744177643
"n_hex": "0x3fffffffffeb"
"n_bit": "2^46 - 2^4 - 2^2 - 1"
"n_fac": "2 * 3 * 263 * 44593627489 + 1"
"nd": 56965173858109
"nd_hex": "0x33cf3cf3cf3d"
"nd_bit": "2^46 - 2^44 + 2^42 - 2^38 + 2^36 - 2^32 + 2^30 - 2^26 + 2^24 - 2^20 + 2^18 - 2^14 + 2^12 - 2^8 + 2^6 - 2^2 + 1"
"r2": 441
"r2_hex": "0x1b9"
"r2_bit": "2^9 - 2^6 - 2^3 + 1"
"znprimroot": 2
- "n": 70368744177271
"n_hex": "0x3ffffffffe77"
"n_bit": "2^46 - 2^9 + 2^7 - 2^3 - 1"
"n_fac": "2 * 3^2 * 5 * 7 * 11 * 1171 * 8671409 + 1"
"nd": 4655438546105
"nd_hex": "0x43bedc2c4b9"
"nd_bit": "2^42 + 2^38 - 2^34 - 2^28 - 2^25 - 2^22 + 2^18 - 2^16 - 2^14 + 2^10 + 2^8 - 2^6 - 2^3 + 1"
"r2": 154449
"r2_hex": "0x25b51"
"r2_bit": "2^17 + 2^15 - 2^13 - 2^10 - 2^8 + 2^6 + 2^4 + 1"
"znprimroot": 3
- "n": 70368744176221
"n_hex": "0x3ffffffffa5d"
"n_bit": "2^46 - 2^11 + 2^9 + 2^7 - 2^5 - 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 7 * 199 * 3011 * 279619 + 1"
"nd": 35940238710283
"nd_hex": "0x20affd29560b"
"nd_bit": "2^45 + 2^40 - 2^38 - 2^36 - 2^26 + 2^24 + 2^21 + 2^19 + 2^17 - 2^15 - 2^13 - 2^11 - 2^9 + 2^4 - 2^2 - 1"
"r2": 2082249
"r2_hex": "0x1fc5c9"
"r2_bit": "2^21 - 2^14 + 2^11 - 2^9 - 2^6 + 2^3 + 1"
"znprimroot": 2
- "n": 70368744177289
"n_hex": "0x3ffffffffe89"
"n_bit": "2^46 - 2^9 + 2^7 + 2^3 + 1"
"n_fac": "2^3 * 3^3 * 1123 * 290099041 + 1"
"nd": 49914895870023
"nd_hex": "0x2d65b7a32847"
"nd_bit": "2^46 - 2^44 - 2^41 - 2^39 - 2^37 + 2^35 - 2^33 - 2^30 - 2^27 - 2^23 + 2^21 + 2^18 - 2^16 + 2^13 + 2^11 + 2^6 + 2^3 - 1"
"r2": 140625
"r2_hex": "0x22551"
"r2_bit": "2^17 + 2^13 + 2^10 + 2^8 + 2^6 + 2^4 + 1"
"znprimroot": 7
- "n": 70368744174769
"n_hex": "0x3ffffffff4b1"
"n_bit": "2^46 - 2^12 + 2^10 + 2^8 - 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3^2 * 13 * 37590141119 + 1"
"nd": 18862226418607
"nd_hex": "0x1127b44e2baf"
"nd_bit": "2^44 + 2^40 + 2^37 + 2^35 - 2^30 - 2^28 + 2^26 + 2^22 + 2^20 - 2^17 + 2^14 - 2^12 - 2^10 - 2^6 - 2^4 - 1"
"r2": 8381025
"r2_hex": "0x7fe261"
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"znprimroot": 7
- "n": 70368744174481
"n_hex": "0x3ffffffff391"
"n_bit": "2^46 - 2^12 + 2^10 - 2^7 + 2^4 + 1"
"n_fac": "2^4 * 3^5 * 5 * 71 * 163 * 312779 + 1"
"nd": 16160713790095
"nd_hex": "0xeb2b59ad28f"
"nd_bit": "2^44 - 2^40 - 2^38 - 2^36 + 2^34 - 2^32 - 2^30 - 2^27 - 2^25 - 2^23 + 2^21 - 2^18 - 2^16 - 2^14 + 2^12 + 2^9 + 2^7 + 2^4 - 1"
"r2": 10131489
"r2_hex": "0x9a9821"
"r2_bit": "2^23 + 2^21 - 2^19 + 2^17 + 2^15 + 2^13 - 2^11 + 2^5 + 1"
"znprimroot": 31
- "n": 70368744173473
"n_hex": "0x3fffffffefa1"
"n_bit": "2^46 - 2^12 - 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 244335917269 + 1"
"nd": 59572489702303
"nd_hex": "0x362e4d164b9f"
"nd_bit": "2^46 - 2^43 - 2^41 + 2^38 - 2^36 - 2^33 + 2^30 + 2^28 - 2^26 + 2^24 + 2^21 - 2^19 - 2^17 + 2^14 + 2^12 - 2^10 - 2^7 + 2^5 - 1"
"r2": 17564481
"r2_hex": "0x10c0341"
"r2_bit": "2^24 + 2^20 - 2^18 + 2^10 - 2^8 + 2^6 + 1"
"znprimroot": 5
- "n": 70368744166561
"n_hex": "0x3fffffffd4a1"
"n_bit": "2^46 - 2^14 + 2^12 + 2^10 + 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 7 * 67 * 104194421 + 1"
"nd": 14976253489311
"nd_hex": "0xd9eee44f09f"
"nd_bit": "2^44 - 2^41 - 2^39 + 2^37 - 2^32 - 2^28 - 2^25 + 2^22 + 2^18 + 2^16 - 2^12 + 2^7 + 2^5 - 1"
"r2": 123276609
"r2_hex": "0x7590d41"
"r2_bit": "2^27 - 2^23 - 2^21 - 2^19 + 2^16 + 2^12 - 2^10 + 2^8 + 2^6 + 1"
"znprimroot": 17
- "n": 70368744177601
"n_hex": "0x3fffffffffc1"
"n_bit": "2^46 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5^2 * 11 * 17 * 31 * 41 * 61681 + 1"
"nd": 65900887404479
"nd_hex": "0x3befbefbefbf"
"nd_bit": "2^46 - 2^42 - 2^36 - 2^30 - 2^24 - 2^18 - 2^12 - 2^6 - 1"
"r2": 3969
"r2_hex": "0xf81"
"r2_bit": "2^12 - 2^7 + 1"
"znprimroot": 29
- "n": 70368744169921
"n_hex": "0x3fffffffe1c1"
"n_bit": "2^46 - 2^13 + 2^9 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 7 * 10471539311c + 1"
"nd": 69759845061055
"nd_hex": "0x3f723ac8d1bf"
"nd_bit": "2^46 - 2^39 - 2^36 + 2^33 + 2^30 - 2^26 - 2^24 - 2^22 + 2^19 + 2^16 - 2^14 + 2^12 + 2^9 - 2^6 - 1"
"r2": 59954049
"r2_hex": "0x392d381"
"r2_bit": "2^26 - 2^23 + 2^20 + 2^18 - 2^16 - 2^14 + 2^12 + 2^10 - 2^7 + 1"
"znprimroot": 39
- "n": 70368744169153
"n_hex": "0x3fffffffdec1"
"n_bit": "2^46 - 2^13 - 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3^2 * 11 * 13 * 97 * 8807437 + 1"
"nd": 64556357013183
"nd_hex": "0x3ab6b2ba4ebf"
"nd_bit": "2^46 - 2^42 - 2^40 - 2^38 - 2^35 - 2^32 - 2^30 - 2^28 + 2^26 - 2^24 - 2^22 - 2^19 + 2^17 + 2^14 + 2^12 - 2^8 - 2^6 - 1"
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"r2_hex": "0x3eb9451db69d"
"r2_bit": "2^46 - 2^40 - 2^38 - 2^35 + 2^32 + 2^30 + 2^26 + 2^24 + 2^21 - 2^17 - 2^14 - 2^11 - 2^9 + 2^7 + 2^5 - 2^2 + 1"
"znprimroot": 19
- "n": 65841848647681
"n_hex": "0x3be200000001"
"n_bit": "2^46 - 2^42 - 2^37 + 2^33 + 1"
"n_fac": "2^33 * 3 * 5 * 7 * 73 + 1"
"nd": 65841848647679
"nd_hex": "0x3be1ffffffff"
"nd_bit": "2^46 - 2^42 - 2^37 + 2^33 - 1"
"r2": 17246583782331
"r2_hex": "0xfaf887ffbbb"
"r2_bit": "2^44 - 2^38 - 2^36 - 2^31 + 2^27 + 2^23 - 2^10 - 2^6 - 2^2 - 1"
"znprimroot": 11
- "n": 64553358458881
"n_hex": "0x3ab600000001"
"n_bit": "2^46 - 2^42 - 2^40 - 2^38 - 2^35 - 2^33 + 1"
"n_fac": "2^33 * 3^2 * 5 * 167 + 1"
"nd": 64553358458879
"nd_hex": "0x3ab5ffffffff"
"nd_bit": "2^46 - 2^42 - 2^40 - 2^38 - 2^35 - 2^33 - 1"
"r2": 50663532524932
"r2_hex": "0x2e1405dbf584"
"r2_bit": "2^46 - 2^44 - 2^41 + 2^36 + 2^34 + 2^27 - 2^25 - 2^21 - 2^18 - 2^11 - 2^9 - 2^7 + 2^2"
"znprimroot": 13
- "n": 70317204570113
"n_hex": "0x3ff400000001"
"n_bit": "2^46 - 2^36 + 2^34 + 1"
"n_fac": "2^34 * 4093 + 1"
"nd": 70317204570111
"nd_hex": "0x3ff3ffffffff"
"nd_bit": "2^46 - 2^36 + 2^34 - 1"
"r2": 18519861203949
"r2_hex": "0x10d7fdbf93ed"
"r2_bit": "2^44 + 2^40 - 2^37 - 2^35 - 2^25 - 2^22 - 2^15 + 2^12 + 2^10 - 2^4 - 2^2 + 1"
"znprimroot": 3
- "n": 70248485093377
"n_hex": "0x3fe400000001"
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"n_fac": "2^34 * 3 * 29 * 47 + 1"
"nd": 70248485093375
"nd_hex": "0x3fe3ffffffff"
"nd_bit": "2^46 - 2^37 + 2^34 - 1"
"r2": 19258427482536
"r2_hex": "0x1183f3baa1a8"
"r2_bit": "2^44 + 2^41 - 2^39 + 2^34 - 2^28 + 2^26 - 2^22 - 2^19 + 2^17 + 2^15 + 2^13 + 2^9 - 2^7 + 2^5 + 2^3"
"znprimroot": 7
- "n": 69114613727233
"n_hex": "0x3edc00000001"
"n_bit": "2^46 - 2^40 - 2^37 - 2^34 + 1"
"n_fac": "2^34 * 3^3 * 149 + 1"
"nd": 69114613727231
"nd_hex": "0x3edbffffffff"
"nd_bit": "2^46 - 2^40 - 2^37 - 2^34 - 1"
"r2": 30213812736031
"r2_hex": "0x1b7ab393501f"
"r2_bit": "2^45 - 2^42 - 2^39 - 2^34 - 2^32 - 2^30 - 2^28 + 2^26 - 2^23 + 2^20 + 2^18 - 2^16 + 2^14 + 2^12 + 2^5 - 1"
"znprimroot": 5
- "n": 64166811402241
"n_hex": "0x3a5c00000001"
"n_bit": "2^46 - 2^43 + 2^41 + 2^39 - 2^37 - 2^34 + 1"
"n_fac": "2^34 * 3^2 * 5 * 83 + 1"
"nd": 64166811402239
"nd_hex": "0x3a5bffffffff"
"nd_bit": "2^46 - 2^43 + 2^41 + 2^39 - 2^37 - 2^34 - 1"
"r2": 40924306673974
"r2_hex": "0x25386ec31136"
"r2_bit": "2^45 + 2^42 + 2^40 + 2^38 - 2^35 + 2^31 - 2^28 - 2^24 - 2^22 + 2^18 - 2^16 + 2^12 + 2^8 + 2^6 - 2^3 - 2"
"znprimroot": 13
- "n": 59528246722561
"n_hex": "0x362400000001"
"n_bit": "2^46 - 2^43 - 2^41 + 2^37 + 2^34 + 1"
"n_fac": "2^34 * 3^2 * 5 * 7 * 11 + 1"
"nd": 59528246722559
"nd_hex": "0x3623ffffffff"
"nd_bit": "2^46 - 2^43 - 2^41 + 2^37 + 2^34 - 1"
"r2": 20995356991024
"r2_hex": "0x13185ccb9e30"
"r2_bit": "2^44 + 2^42 - 2^40 + 2^37 - 2^35 + 2^31 - 2^29 - 2^26 + 2^24 - 2^22 + 2^20 - 2^18 - 2^15 + 2^13 - 2^9 + 2^6 - 2^4"
"znprimroot": 39
- "n": 68341519613953
"n_hex": "0x3e2800000001"
"n_bit": "2^46 - 2^41 + 2^37 + 2^35 + 1"
"n_fac": "2^35 * 3^2 * 13 * 17 + 1"
"nd": 68341519613951
"nd_hex": "0x3e27ffffffff"
"nd_bit": "2^46 - 2^41 + 2^37 + 2^35 - 1"
"r2": 13477603056129
"r2_hex": "0xc41ffbe1a01"
"r2_bit": "2^44 - 2^42 + 2^38 + 2^33 - 2^22 - 2^17 + 2^13 - 2^11 + 2^9 + 1"
"znprimroot": 7
- "n": 55044300865537
"n_hex": "0x321000000001"
"n_bit": "2^46 - 2^44 + 2^41 + 2^36 + 1"
"n_fac": "2^36 * 3^2 * 89 + 1"
"nd": 55044300865535
"nd_hex": "0x320fffffffff"
"nd_bit": "2^46 - 2^44 + 2^41 + 2^36 - 1"
"r2": 8034430707026
"r2_hex": "0x74ea9636552"
"r2_bit": "2^43 - 2^40 + 2^38 + 2^36 - 2^33 + 2^31 + 2^29 + 2^27 + 2^25 - 2^23 - 2^21 + 2^18 - 2^15 - 2^13 + 2^10 + 2^8 + 2^6 + 2^4 + 2"
"znprimroot": 5
- "n": 50508815400961
"n_hex": "0x2df000000001"
"n_bit": "2^46 - 2^44 - 2^41 - 2^36 + 1"
"n_fac": "2^36 * 3 * 5 * 7^2 + 1"
"nd": 50508815400959
"nd_hex": "0x2defffffffff"
"nd_bit": "2^46 - 2^44 - 2^41 - 2^36 - 1"
"r2": 27787818994873
"r2_hex": "0x1945db148cb9"
"r2_bit": "2^45 - 2^43 + 2^40 + 2^38 + 2^35 - 2^33 - 2^29 - 2^26 - 2^24 + 2^20 + 2^18 + 2^15 + 2^12 - 2^10 + 2^8 - 2^6 - 2^3 + 1"
"znprimroot": 17
- "n": 70093866270721
"n_hex": "0x3fc000000001"
"n_bit": "2^46 - 2^38 + 1"
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"nd": 70093866270719
"nd_hex": "0x3fbfffffffff"
"nd_bit": "2^46 - 2^38 - 1"
"r2": 17041352277953
"r2_hex": "0xf7fbfbfbfc1"
"r2_bit": "2^44 - 2^39 - 2^30 - 2^22 - 2^14 - 2^6 + 1"
"znprimroot": 7
- "n": 37108517437441
"n_hex": "0x21c000000001"
"n_bit": "2^45 + 2^41 - 2^38 + 1"
"n_fac": "2^38 * 3^3 * 5 + 1"
"nd": 37108517437439
"nd_hex": "0x21bfffffffff"
"nd_bit": "2^45 + 2^41 - 2^38 - 1"
"r2": 7847255210094
"r2_hex": "0x72314dbf86e"
"r2_bit": "2^43 - 2^40 + 2^37 + 2^34 - 2^32 + 2^28 + 2^26 + 2^24 - 2^21 - 2^18 - 2^11 + 2^7 - 2^4 - 2"
"znprimroot": 11
- "n": 28862180229121
"n_hex": "0x1a4000000001"
"n_bit": "2^45 - 2^43 + 2^41 + 2^38 + 1"
"n_fac": "2^38 * 3 * 5 * 7 + 1"
"nd": 28862180229119
"nd_hex": "0x1a3fffffffff"
"nd_bit": "2^45 - 2^43 + 2^41 + 2^38 - 1"
"r2": 19199567328838
"r2_hex": "0x11763f63f646"
"r2_bit": "2^44 + 2^41 - 2^39 - 2^35 - 2^33 + 2^30 - 2^23 - 2^21 + 2^18 - 2^11 - 2^9 + 2^6 + 2^3 - 2"
"znprimroot": 19
- "n": 44530220924929
"n_hex": "0x288000000001"
"n_bit": "2^45 + 2^43 + 2^39 + 1"
"n_fac": "2^39 * 3^4 + 1"
"nd": 44530220924927
"nd_hex": "0x287fffffffff"
"nd_bit": "2^45 + 2^43 + 2^39 - 1"
"r2": 400439419995
"r2_hex": "0x5d3c0ca45b"
"r2_bit": "2^39 - 2^37 - 2^34 + 2^32 + 2^30 - 2^26 + 2^20 - 2^18 + 2^15 + 2^13 + 2^10 + 2^7 - 2^5 - 2^2 - 1"
"znprimroot": 7
- "n": 62672162783233
"n_hex": "0x390000000001"
"n_bit": "2^46 - 2^43 + 2^40 + 1"
"n_fac": "2^40 * 3 * 19 + 1"
"nd": 62672162783231
"nd_hex": "0x38ffffffffff"
"nd_bit": "2^46 - 2^43 + 2^40 - 1"
"r2": 30940642999172
"r2_hex": "0x1c23ee08fb84"
"r2_bit": "2^45 - 2^42 + 2^37 + 2^34 - 2^28 - 2^25 + 2^19 + 2^16 - 2^10 - 2^7 + 2^2"
"znprimroot": 5
- "n": 50577534877697
"n_hex": "0x2e0000000001"
"n_bit": "2^46 - 2^44 - 2^41 + 1"
"n_fac": "2^41 * 23 + 1"
"nd": 50577534877695
"nd_hex": "0x2dffffffffff"
"nd_bit": "2^46 - 2^44 - 2^41 - 1"
"r2": 31838032352125
"r2_hex": "0x1cf4de9bd37d"
"r2_bit": "2^45 - 2^42 + 2^40 - 2^36 + 2^34 + 2^32 - 2^29 - 2^25 + 2^23 + 2^21 - 2^18 - 2^14 + 2^12 + 2^10 - 2^7 - 2^2 + 1"
"znprimroot": 3
- "n": 46179488366593
"n_hex": "0x2a0000000001"
"n_bit": "2^45 + 2^43 + 2^41 + 1"
"n_fac": "2^41 * 3 * 7 + 1"
"nd": 46179488366591
"nd_hex": "0x29ffffffffff"
"nd_bit": "2^45 + 2^43 + 2^41 - 1"
"r2": 2722600221162
"r2_hex": "0x279e79e79ea"
"r2_bit": "2^41 + 2^39 - 2^35 + 2^33 - 2^29 + 2^27 - 2^23 + 2^21 - 2^17 + 2^15 - 2^11 + 2^9 - 2^5 + 2^3 + 2"
"znprimroot": 11
- "n": 39582418599937
"n_hex": "0x240000000001"
"n_bit": "2^45 + 2^42 + 1"
"n_fac": "2^42 * 3^2 + 1"
"nd": 39582418599935
"nd_hex": "0x23ffffffffff"
"nd_bit": "2^45 + 2^42 - 1"
"r2": 11239452195047
"r2_hex": "0xa38e38e38e7"
"r2_bit": "2^43 + 2^41 + 2^38 - 2^35 + 2^32 - 2^29 + 2^26 - 2^23 + 2^20 - 2^17 + 2^14 - 2^11 + 2^8 - 2^5 + 2^3 - 1"
"znprimroot": 5
Raw
result_prime_0047.yaml
- "r": 47
"primes":
- "n": 140737488355213
"n_hex": "0x7fffffffff8d"
"n_bit": "2^47 - 2^7 + 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3 * 7 * 1675446289943 + 1"
"nd": 52623582602427
"nd_hex": "0x2fdc61f2a4bb"
"nd_bit": "2^46 - 2^44 - 2^37 - 2^34 + 2^31 - 2^29 + 2^25 - 2^20 + 2^17 + 2^15 + 2^13 + 2^10 + 2^8 - 2^6 - 2^2 - 1"
"r2": 13225
"r2_hex": "0x33a9"
"r2_bit": "2^14 - 2^12 + 2^10 - 2^7 + 2^5 + 2^3 + 1"
"znprimroot": 5
- "n": 140737488354613
"n_hex": "0x7ffffffffd35"
"n_bit": "2^47 - 2^10 + 2^8 + 2^6 - 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 37 * 105658775041c + 1"
"nd": 76372231443171
"nd_hex": "0x4575cbb9d2e3"
"nd_bit": "2^46 + 2^43 - 2^41 - 2^39 - 2^35 - 2^33 - 2^30 + 2^28 - 2^26 - 2^22 - 2^19 + 2^17 - 2^14 + 2^12 + 2^10 - 2^8 - 2^5 + 2^2 - 1"
"r2": 511225
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"znprimroot": 2
- "n": 140737488353821
"n_hex": "0x7ffffffffa1d"
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"n_fac": "2^2 * 3^6 * 5 * 9652776979c + 1"
"nd": 68080709363659
"nd_hex": "0x3deb467f67cb"
"nd_bit": "2^46 - 2^41 - 2^36 - 2^34 - 2^32 + 2^30 + 2^27 - 2^25 + 2^23 - 2^15 - 2^13 + 2^11 - 2^6 + 2^4 - 2^2 - 1"
"r2": 2271049
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"r2_bit": "2^21 + 2^17 + 2^15 + 2^13 + 2^11 - 2^8 + 2^6 + 2^3 + 1"
"znprimroot": 13
- "n": 140737488353701
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"n_bit": "2^47 - 2^11 + 2^9 - 2^7 + 2^5 + 2^2 + 1"
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"nd": 89961270983123
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"r2": 2647129
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"znprimroot": 11
- "n": 140737488344461
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"n_fac": "2^2 * 3^2 * 5 * 7 * 43 * 953 * 2725699 + 1"
"nd": 26678865005243
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"nd_bit": "2^45 - 2^43 + 2^38 + 2^34 - 2^31 + 2^29 + 2^27 + 2^22 + 2^19 - 2^17 - 2^15 + 2^12 - 2^10 - 2^8 - 2^6 - 2^2 - 1"
"r2": 118091689
"r2_hex": "0x709efa9"
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"znprimroot": 2
- "n": 140737488352921
"n_hex": "0x7ffffffff699"
"n_bit": "2^47 - 2^11 - 2^9 + 2^7 + 2^5 - 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5 * 390937467647 + 1"
"nd": 119278968111703
"nd_hex": "0x6c7bcc860257"
"nd_bit": "2^47 - 2^44 - 2^42 + 2^39 - 2^34 - 2^30 + 2^28 - 2^26 + 2^23 + 2^19 - 2^17 + 2^9 + 2^7 - 2^5 - 2^3 - 1"
"r2": 5793649
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"znprimroot": 7
- "n": 140737488340681
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"n_bit": "2^47 - 2^14 + 2^11 - 2^8 - 2^6 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 5 * 7 * 11 * 139 * 36525971 + 1"
"nd": 47514636438663
"nd_hex": "0x2b36dd06cc87"
"nd_bit": "2^46 - 2^44 - 2^42 - 2^40 + 2^38 - 2^35 - 2^32 - 2^29 - 2^26 + 2^24 + 2^19 - 2^16 - 2^14 + 2^12 - 2^10 + 2^7 + 2^3 - 1"
"r2": 214534609
"r2_hex": "0xcc989d1"
"r2_bit": "2^28 - 2^26 + 2^24 - 2^22 + 2^19 + 2^17 - 2^15 + 2^11 + 2^9 - 2^6 + 2^4 + 1"
"znprimroot": 37
- "n": 140737488353713
"n_hex": "0x7ffffffff9b1"
"n_bit": "2^47 - 2^11 + 2^9 - 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3^3 * 31 * 461 * 22796251 + 1"
"nd": 36861893234863
"nd_hex": "0x2186940d50af"
"nd_bit": "2^45 + 2^41 - 2^39 + 2^35 - 2^33 + 2^31 + 2^28 + 2^26 + 2^20 - 2^18 + 2^16 + 2^14 + 2^12 + 2^8 - 2^6 - 2^4 - 1"
"r2": 2608225
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"znprimroot": 5
- "n": 140737488349681
"n_hex": "0x7fffffffe9f1"
"n_bit": "2^47 - 2^13 + 2^11 + 2^9 - 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5 * 311 * 628516829 + 1"
"nd": 13084324665583
"nd_hex": "0xbe66e8618ef"
"nd_bit": "2^44 - 2^42 - 2^37 + 2^35 - 2^33 + 2^31 - 2^28 - 2^25 + 2^23 + 2^19 - 2^17 + 2^13 - 2^11 + 2^8 - 2^4 - 1"
"r2": 31888609
"r2_hex": "0x1e694e1"
"r2_bit": "2^25 - 2^21 + 2^19 - 2^17 + 2^15 + 2^12 + 2^10 + 2^8 - 2^5 + 1"
"znprimroot": 7
- "n": 140737488318001
"n_hex": "0x7fffffff6e31"
"n_bit": "2^47 - 2^15 - 2^12 - 2^9 + 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5^3 * 7 * 31 * 197 * 182899 + 1"
"nd": 53132389045551
"nd_hex": "0x3052d92cd52f"
"nd_bit": "2^46 - 2^44 + 2^38 + 2^36 + 2^34 - 2^32 - 2^29 - 2^27 + 2^24 + 2^22 - 2^20 - 2^18 + 2^16 - 2^14 + 2^12 + 2^10 + 2^8 + 2^6 - 2^4 - 1"
"r2": 1393304929
"r2_hex": "0x530c2561"
"r2_bit": "2^30 + 2^28 + 2^26 - 2^24 + 2^20 - 2^18 + 2^13 + 2^11 - 2^9 - 2^7 - 2^5 + 1"
"znprimroot": 23
- "n": 140737488353569
"n_hex": "0x7ffffffff921"
"n_bit": "2^47 - 2^11 + 2^8 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 17 * 373 * 733 * 105137 + 1"
"nd": 71928938050847
"nd_hex": "0x416b42cd351f"
"nd_bit": "2^46 + 2^41 - 2^39 - 2^36 - 2^34 - 2^32 + 2^30 + 2^26 - 2^24 - 2^22 + 2^20 - 2^18 + 2^16 + 2^14 - 2^12 + 2^10 + 2^8 + 2^5 - 1"
"r2": 3094081
"r2_hex": "0x2f3641"
"r2_bit": "2^22 - 2^20 - 2^16 + 2^14 - 2^11 - 2^9 + 2^6 + 1"
"znprimroot": 22
- "n": 140737488346561
"n_hex": "0x7fffffffddc1"
"n_bit": "2^47 - 2^13 - 2^9 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 7 * 2671 * 7840913 + 1"
"nd": 86574344097215
"nd_hex": "0x4ebd2906cdbf"
"nd_bit": "2^46 + 2^44 - 2^40 - 2^38 - 2^34 + 2^32 + 2^29 + 2^27 + 2^24 + 2^19 - 2^16 - 2^14 + 2^12 - 2^9 - 2^6 - 1"
"r2": 76860289
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"r2_bit": "2^26 + 2^23 + 2^20 + 2^18 + 2^16 - 2^14 + 2^12 - 2^10 - 2^7 + 1"
"znprimroot": 13
- "n": 140737488292801
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"n_fac": "2^6 * 3^3 * 5^2 * 7 * 6619 * 70313 + 1"
"nd": 82247486077887
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"nd_bit": "2^46 + 2^44 - 2^42 - 2^40 - 2^38 + 2^36 - 2^33 - 2^30 - 2^26 + 2^22 - 2^20 + 2^16 - 2^10 - 2^6 - 1"
"r2": 3909625729
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"r2_bit": "2^32 - 2^29 + 2^27 + 2^24 + 2^19 + 2^13 + 2^11 - 2^7 + 1"
"znprimroot": 59
- "n": 140737488355201
"n_hex": "0x7fffffffff81"
"n_bit": "2^47 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5^2 * 11 * 17 * 31 * 41 * 61681 + 1"
"nd": 136304811556735
"nd_hex": "0x7bf7efdfbf7f"
"nd_bit": "2^47 - 2^42 - 2^35 - 2^28 - 2^21 - 2^14 - 2^7 - 1"
"r2": 16129
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"r2_bit": "2^14 - 2^8 + 1"
"znprimroot": 7
- "n": 140737488340609
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"n_bit": "2^47 - 2^14 + 2^11 - 2^9 + 2^7 + 1"
"n_fac": "2^7 * 3^2 * 1549 * 78868921 + 1"
"nd": 83186096113279
"nd_hex": "0x4ba845b5867f"
"nd_bit": "2^46 + 2^44 - 2^42 - 2^39 + 2^37 + 2^35 + 2^30 + 2^27 - 2^25 - 2^22 - 2^19 - 2^17 - 2^15 + 2^11 - 2^9 + 2^7 - 1"
"r2": 216648961
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"r2_bit": "2^45 - 2^37 + 2^34 - 2^32 + 2^29 + 2^26 - 2^24 - 2^21 + 2^18 + 2^16 - 2^14 - 2^10 - 2^4 - 2^2 - 1"
"znprimroot": 11
- "n": 140381006069761
"n_hex": "0x7fad00000001"
"n_bit": "2^47 - 2^38 - 2^36 - 2^34 + 2^32 + 1"
"n_fac": "2^32 * 3 * 5 * 2179 + 1"
"nd": 140381006069759
"nd_hex": "0x7facffffffff"
"nd_bit": "2^47 - 2^38 - 2^36 - 2^34 + 2^32 - 1"
"r2": 134530355364646
"r2_hex": "0x7a5aca0b0326"
"r2_bit": "2^47 - 2^43 + 2^41 + 2^39 - 2^37 - 2^34 - 2^32 - 2^30 + 2^27 + 2^25 + 2^20 - 2^18 - 2^16 + 2^10 - 2^8 + 2^5 + 2^3 - 2"
"znprimroot": 11
- "n": 136644384522241
"n_hex": "0x7c4700000001"
"n_bit": "2^47 - 2^42 + 2^38 + 2^35 - 2^32 + 1"
"n_fac": "2^32 * 3^2 * 5 * 7 * 101 + 1"
"nd": 136644384522239
"nd_hex": "0x7c46ffffffff"
"nd_bit": "2^47 - 2^42 + 2^38 + 2^35 - 2^32 - 1"
"r2": 121588176666301
"r2_hex": "0x6e9574143ebd"
"r2_bit": "2^47 - 2^44 - 2^41 + 2^39 + 2^37 - 2^35 - 2^33 - 2^31 - 2^28 + 2^26 + 2^20 + 2^18 + 2^14 - 2^8 - 2^6 - 2^2 + 1"
"znprimroot": 11
- "n": 140316581560321
"n_hex": "0x7f9e00000001"
"n_bit": "2^47 - 2^39 + 2^37 - 2^33 + 1"
"n_fac": "2^33 * 3^3 * 5 * 11^2 + 1"
"nd": 140316581560319
"nd_hex": "0x7f9dffffffff"
"nd_bit": "2^47 - 2^39 + 2^37 - 2^33 - 1"
"r2": 20434191802820
"r2_hex": "0x1295b4be61c4"
"r2_bit": "2^44 + 2^41 + 2^39 + 2^37 - 2^35 - 2^33 - 2^30 - 2^28 + 2^26 + 2^24 - 2^22 - 2^17 + 2^15 - 2^13 + 2^9 - 2^6 + 2^2"
"znprimroot": 7
- "n": 134389526691841
"n_hex": "0x7a3a00000001"
"n_bit": "2^47 - 2^43 + 2^41 + 2^38 - 2^35 + 2^33 + 1"
"n_fac": "2^33 * 3 * 5 * 7 * 149 + 1"
"nd": 134389526691839
"nd_hex": "0x7a39ffffffff"
"nd_bit": "2^47 - 2^43 + 2^41 + 2^38 - 2^35 + 2^33 - 1"
"r2": 10471928590749
"r2_hex": "0x9862f95719d"
"r2_bit": "2^43 + 2^41 - 2^39 + 2^35 - 2^33 + 2^30 - 2^28 - 2^23 + 2^21 - 2^19 - 2^17 - 2^15 - 2^12 + 2^9 - 2^7 + 2^5 - 2^2 + 1"
"znprimroot": 19
- "n": 131683697295361
"n_hex": "0x77c400000001"
"n_bit": "2^47 - 2^43 - 2^38 + 2^34 + 1"
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"nd": 131683697295359
"nd_hex": "0x77c3ffffffff"
"nd_bit": "2^47 - 2^43 - 2^38 + 2^34 - 1"
"r2": 87716402296693
"r2_hex": "0x4fc710fff775"
"r2_bit": "2^46 + 2^44 - 2^38 + 2^35 - 2^32 + 2^28 + 2^24 - 2^11 - 2^7 - 2^4 + 2^2 + 1"
"znprimroot": 11
- "n": 140496970186753
"n_hex": "0x7fc800000001"
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"nd": 140496970186751
"nd_hex": "0x7fc7ffffffff"
"nd_bit": "2^47 - 2^38 + 2^35 - 1"
"r2": 77515158012751
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"znprimroot": 5
- "n": 140084653326337
"n_hex": "0x7f6800000001"
"n_bit": "2^47 - 2^39 - 2^37 + 2^35 + 1"
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"nd": 140084653326335
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"nd_bit": "2^47 - 2^39 - 2^37 + 2^35 - 1"
"r2": 22055909632073
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"r2_bit": "2^44 + 2^42 + 2^36 - 2^32 + 2^30 + 2^27 + 2^25 + 2^23 + 2^21 + 2^19 + 2^15 + 2^13 + 2^11 + 2^6 + 2^3 + 1"
"znprimroot": 5
- "n": 119056493445121
"n_hex": "0x6c4800000001"
"n_bit": "2^47 - 2^44 - 2^42 + 2^38 + 2^35 + 1"
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"nd": 119056493445119
"nd_hex": "0x6c47ffffffff"
"nd_bit": "2^47 - 2^44 - 2^42 + 2^38 + 2^35 - 1"
"r2": 12235180555358
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"r2_bit": "2^44 - 2^42 - 2^40 + 2^37 + 2^32 - 2^30 - 2^27 + 2^25 - 2^23 + 2^21 - 2^19 - 2^16 + 2^14 - 2^10 + 2^7 - 2^5 - 2"
"znprimroot": 13
- "n": 139156940390401
"n_hex": "0x7e9000000001"
"n_bit": "2^47 - 2^41 + 2^39 + 2^36 + 1"
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"nd": 139156940390399
"nd_hex": "0x7e8fffffffff"
"nd_bit": "2^47 - 2^41 + 2^39 + 2^36 - 1"
"r2": 70282072798118
"r2_hex": "0x3febd1fbb3a6"
"r2_bit": "2^46 - 2^36 - 2^34 - 2^30 + 2^28 + 2^25 - 2^18 - 2^14 - 2^12 + 2^10 - 2^7 + 2^5 + 2^3 - 2"
"znprimroot": 13
- "n": 50508815400961
"n_hex": "0x2df000000001"
"n_bit": "2^46 - 2^44 - 2^41 - 2^36 + 1"
"n_fac": "2^36 * 3 * 5 * 7^2 + 1"
"nd": 50508815400959
"nd_hex": "0x2defffffffff"
"nd_bit": "2^46 - 2^44 - 2^41 - 2^36 - 1"
"r2": 10133645177570
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"r2_bit": "2^43 + 2^40 + 2^38 - 2^35 - 2^31 - 2^28 - 2^26 + 2^22 + 2^20 + 2^17 + 2^14 - 2^12 + 2^10 - 2^8 - 2^5 + 2"
"znprimroot": 17
- "n": 140050293587969
"n_hex": "0x7f6000000001"
"n_bit": "2^47 - 2^39 - 2^37 + 1"
"n_fac": "2^37 * 1019 + 1"
"nd": 140050293587967
"nd_hex": "0x7f5fffffffff"
"nd_bit": "2^47 - 2^39 - 2^37 - 1"
"r2": 74488540874233
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"r2_bit": "2^46 + 2^42 - 2^38 - 2^32 + 2^30 - 2^27 - 2^24 + 2^18 + 2^16 - 2^14 + 2^11 - 2^9 - 2^3 + 1"
"znprimroot": 3
- "n": 134002979635201
"n_hex": "0x79e000000001"
"n_bit": "2^47 - 2^43 + 2^41 - 2^37 + 1"
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"nd": 134002979635199
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"nd_bit": "2^47 - 2^43 + 2^41 - 2^37 - 1"
"r2": 2960082650215
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"r2_bit": "2^42 - 2^40 - 2^38 - 2^36 + 2^32 + 2^30 - 2^28 + 2^26 - 2^24 - 2^22 - 2^20 - 2^18 + 2^16 - 2^14 + 2^10 + 2^7 - 2^5 + 2^3 - 1"
"znprimroot": 11
- "n": 132353712193537
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"n_bit": "2^47 - 2^43 + 2^39 - 2^37 + 1"
"n_fac": "2^37 * 3^2 * 107 + 1"
"nd": 132353712193535
"nd_hex": "0x785fffffffff"
"nd_bit": "2^47 - 2^43 + 2^39 - 2^37 - 1"
"r2": 24620268936188
"r2_hex": "0x16645a625bfc"
"r2_bit": "2^45 - 2^43 - 2^41 + 2^39 - 2^37 + 2^34 + 2^31 - 2^29 - 2^27 + 2^25 + 2^23 - 2^21 + 2^17 + 2^15 - 2^13 - 2^10 - 2^2"
"znprimroot": 5
- "n": 138813343006721
"n_hex": "0x7e4000000001"
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"nd": 138813343006719
"nd_hex": "0x7e3fffffffff"
"nd_bit": "2^47 - 2^41 + 2^38 - 1"
"r2": 117346194943426
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"r2_bit": "2^47 - 2^44 - 2^42 - 2^40 - 2^38 - 2^35 + 2^33 - 2^30 + 2^27 + 2^25 + 2^22 + 2^18 - 2^12 - 2^9 - 2^6 + 2"
"znprimroot": 3
- "n": 28862180229121
"n_hex": "0x1a4000000001"
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"nd": 28862180229119
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"nd_bit": "2^45 - 2^43 + 2^41 + 2^38 - 1"
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"r2_hex": "0x1158fd8fd916"
"r2_bit": "2^44 + 2^41 - 2^39 - 2^37 - 2^35 + 2^32 - 2^25 - 2^23 + 2^20 - 2^13 - 2^11 + 2^8 + 2^5 - 2^3 - 2"
"znprimroot": 19
- "n": 103903848824833
"n_hex": "0x5e8000000001"
"n_bit": "2^47 - 2^45 - 2^41 + 2^39 + 1"
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"nd": 103903848824831
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"nd_bit": "2^47 - 2^45 - 2^41 + 2^39 - 1"
"r2": 18278653621548
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"r2_bit": "2^44 + 2^39 + 2^37 - 2^30 + 2^28 + 2^26 + 2^23 + 2^21 + 2^19 - 2^12 + 2^10 + 2^8 + 2^6 - 2^4 - 2^2"
"znprimroot": 10
- "n": 90709709291521
"n_hex": "0x528000000001"
"n_bit": "2^46 + 2^44 + 2^41 + 2^39 + 1"
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"nd": 90709709291519
"nd_hex": "0x527fffffffff"
"nd_bit": "2^46 + 2^44 + 2^41 + 2^39 - 1"
"r2": 16939142774588
"r2_hex": "0xf67f3967f3c"
"r2_bit": "2^44 - 2^39 - 2^37 + 2^35 - 2^28 + 2^26 - 2^23 + 2^21 - 2^19 - 2^17 + 2^15 - 2^8 + 2^6 - 2^2"
"znprimroot": 7
- "n": 74217034874881
"n_hex": "0x438000000001"
"n_bit": "2^46 + 2^42 - 2^39 + 1"
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"nd": 74217034874879
"nd_hex": "0x437fffffffff"
"nd_bit": "2^46 + 2^42 - 2^39 - 1"
"r2": 1400859259096
"r2_hex": "0x14629b7f0d8"
"r2_bit": "2^40 + 2^38 + 2^35 - 2^33 + 2^29 + 2^27 + 2^25 - 2^22 - 2^19 - 2^12 + 2^8 - 2^5 - 2^3"
"znprimroot": 11
- "n": 113249697660929
"n_hex": "0x670000000001"
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"nd": 113249697660927
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"nd_bit": "2^47 - 2^45 + 2^43 - 2^40 - 1"
"r2": 60398415436474
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"r2_bit": "2^46 - 2^43 - 2^40 - 2^36 - 2^33 + 2^31 + 2^29 - 2^27 + 2^25 + 2^21 - 2^19 + 2^16 - 2^13 - 2^10 - 2^8 - 2^6 - 2^3 + 2"
"znprimroot": 3
- "n": 96757023244289
"n_hex": "0x580000000001"
"n_bit": "2^47 - 2^45 - 2^43 + 1"
"n_fac": "2^43 * 11 + 1"
"nd": 96757023244287
"nd_hex": "0x57ffffffffff"
"nd_bit": "2^47 - 2^45 - 2^43 - 1"
"r2": 6397158561608
"r2_hex": "0x5d1745d1748"
"r2_bit": "2^43 - 2^41 - 2^38 + 2^36 + 2^33 - 2^31 - 2^28 + 2^26 + 2^23 - 2^21 - 2^18 + 2^16 + 2^13 - 2^11 - 2^8 + 2^6 + 2^3"
"znprimroot": 3
- "n": 79164837199873
"n_hex": "0x480000000001"
"n_bit": "2^46 + 2^43 + 1"
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"nd": 79164837199871
"nd_hex": "0x47ffffffffff"
"nd_bit": "2^46 + 2^43 - 1"
"r2": 57663276478923
"r2_hex": "0x3471c71c71cb"
"r2_bit": "2^46 - 2^44 + 2^42 + 2^39 - 2^36 + 2^33 - 2^30 + 2^27 - 2^24 + 2^21 - 2^18 + 2^15 - 2^12 + 2^9 - 2^6 + 2^4 - 2^2 - 1"
"znprimroot": 5
Raw
result_prime_0048.yaml
- "r": 48
"primes":
- "n": 281474976710563
"n_hex": "0xffffffffffa3"
"n_bit": "2^48 - 2^7 + 2^5 + 2^2 - 1"
"n_fac": "2 * 3 * 359 * 130675476653 + 1"
"nd": 269368526099445
"nd_hex": "0xf4fd3f4fd3f5"
"nd_bit": "2^48 - 2^44 + 2^42 + 2^40 - 2^34 + 2^32 + 2^30 - 2^24 + 2^22 + 2^20 - 2^14 + 2^12 + 2^10 - 2^4 + 2^2 + 1"
"r2": 8649
"r2_hex": "0x21c9"
"r2_bit": "2^13 + 2^9 - 2^6 + 2^3 + 1"
"znprimroot": 2
- "n": 281474976710491
"n_hex": "0xffffffffff5b"
"n_bit": "2^48 - 2^7 - 2^5 - 2^2 - 1"
"n_fac": "2 * 3 * 5 * 9382499223683c + 1"
"nd": 49471359543085
"nd_hex": "0x2cfe72cfe72d"
"nd_bit": "2^46 - 2^44 - 2^42 + 2^40 - 2^33 + 2^31 - 2^28 + 2^26 - 2^24 - 2^22 + 2^20 - 2^13 + 2^11 - 2^8 + 2^6 - 2^4 - 2^2 + 1"
"r2": 27225
"r2_hex": "0x6a59"
"r2_bit": "2^15 - 2^13 + 2^11 + 2^9 + 2^7 - 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 281474976710467
"n_hex": "0xffffffffff43"
"n_bit": "2^48 - 2^8 + 2^6 + 2^2 - 1"
"n_fac": "2 * 3^2 * 7 * 11^3 * 197 * 727 * 11719 + 1"
"nd": 186160698882709
"nd_hex": "0xa94fea53fa95"
"nd_bit": "2^47 + 2^45 + 2^43 + 2^40 + 2^38 + 2^36 - 2^29 + 2^27 + 2^25 + 2^22 + 2^20 + 2^18 - 2^11 + 2^9 + 2^7 + 2^4 + 2^2 + 1"
"r2": 35721
"r2_hex": "0x8b89"
"r2_bit": "2^15 + 2^12 - 2^10 - 2^7 + 2^3 + 1"
"znprimroot": 2
- "n": 281474976710131
"n_hex": "0xfffffffffdf3"
"n_bit": "2^48 - 2^9 - 2^4 + 2^2 - 1"
"n_fac": "2 * 3 * 5 * 7 * 1340357031953 + 1"
"nd": 55758852529349
"nd_hex": "0x32b65e991cc5"
"nd_bit": "2^46 - 2^44 + 2^42 - 2^40 - 2^38 - 2^35 - 2^33 + 2^31 - 2^29 - 2^25 + 2^23 + 2^21 - 2^19 + 2^16 + 2^13 - 2^10 + 2^8 - 2^6 + 2^2 + 1"
"r2": 275625
"r2_hex": "0x434a9"
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"znprimroot": 3
- "n": 281474976709891
"n_hex": "0xfffffffffd03"
"n_bit": "2^48 - 2^10 + 2^8 + 2^2 - 1"
"n_fac": "2 * 3^2 * 5 * 17 * 37 * 61 * 271 * 300779 + 1"
"nd": 281107035564629
"nd_hex": "0xffaa54ffaa55"
"nd_bit": "2^48 - 2^39 + 2^37 + 2^35 + 2^33 + 2^30 + 2^28 + 2^26 + 2^24 - 2^15 + 2^13 + 2^11 + 2^9 + 2^6 + 2^4 + 2^2 + 1"
"r2": 585225
"r2_hex": "0x8ee09"
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"znprimroot": 2
- "n": 281474976709711
"n_hex": "0xfffffffffc4f"
"n_bit": "2^48 - 2^10 + 2^6 + 2^4 - 1"
"n_fac": "2 * 3^2 * 5 * 7^2 * 63826525331 + 1"
"nd": 93527135118673
"nd_hex": "0x550ffbaa6551"
"nd_bit": "2^46 + 2^44 + 2^42 + 2^40 + 2^36 - 2^26 - 2^23 + 2^21 + 2^19 + 2^17 + 2^15 - 2^13 + 2^10 + 2^8 + 2^6 + 2^4 + 1"
"r2": 893025
"r2_hex": "0xda061"
"r2_bit": "2^20 - 2^17 - 2^15 + 2^13 + 2^7 - 2^5 + 1"
"znprimroot": 6
- "n": 281474976710597
"n_hex": "0xffffffffffc5"
"n_bit": "2^48 - 2^6 + 2^2 + 1"
"n_fac": "2^2 * 797 * 2459 * 35905663 + 1"
"nd": 181288968050931
"nd_hex": "0xa4e1a08ad8f3"
"nd_bit": "2^47 + 2^45 + 2^42 + 2^40 - 2^37 + 2^33 - 2^31 + 2^29 + 2^23 + 2^20 - 2^18 - 2^16 - 2^13 - 2^11 + 2^8 - 2^4 + 2^2 - 1"
"r2": 3481
"r2_hex": "0xd99"
"r2_bit": "2^12 - 2^9 - 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 281474976710509
"n_hex": "0xffffffffff6d"
"n_bit": "2^48 - 2^7 - 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3 * 7 * 3350892579887c + 1"
"nd": 118717337116059
"nd_hex": "0x6bf908b51d9b"
"nd_bit": "2^47 - 2^44 - 2^42 - 2^35 + 2^32 + 2^27 + 2^24 - 2^22 - 2^20 + 2^18 + 2^16 + 2^13 - 2^9 - 2^7 + 2^5 - 2^2 - 1"
"r2": 21609
"r2_hex": "0x5469"
"r2_bit": "2^14 + 2^12 + 2^10 + 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 2
- "n": 281474976710413
"n_hex": "0xffffffffff0d"
"n_bit": "2^48 - 2^8 + 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 7818749353067 + 1"
"nd": 19691665037371
"nd_hex": "0x11e8d2b3183b"
"nd_bit": "2^44 + 2^41 - 2^37 + 2^35 + 2^32 - 2^30 + 2^28 + 2^26 - 2^24 - 2^22 - 2^20 + 2^18 - 2^16 + 2^13 - 2^11 + 2^6 - 2^2 - 1"
"r2": 59049
"r2_hex": "0xe6a9"
"r2_bit": "2^16 - 2^13 + 2^11 - 2^9 + 2^7 + 2^5 + 2^3 + 1"
"znprimroot": 5
- "n": 281474976709741
"n_hex": "0xfffffffffc6d"
"n_bit": "2^48 - 2^10 + 2^7 - 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 11^2 * 2287 * 16952627 + 1"
"nd": 147351381250715
"nd_hex": "0x8603eabc929b"
"nd_bit": "2^47 + 2^43 - 2^41 + 2^34 - 2^28 - 2^26 - 2^24 - 2^22 - 2^18 + 2^15 + 2^12 + 2^9 + 2^7 + 2^5 - 2^2 - 1"
"r2": 837225
"r2_hex": "0xcc669"
"r2_bit": "2^20 - 2^18 + 2^16 - 2^14 + 2^11 - 2^9 + 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 2
- "n": 281474976708901
"n_hex": "0xfffffffff925"
"n_bit": "2^48 - 2^11 + 2^8 + 2^5 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5^2 * 13 * 59 * 269 * 431 * 3517 + 1"
"nd": 93664607634771
"nd_hex": "0x552ffdaa8553"
"nd_bit": "2^46 + 2^44 + 2^42 + 2^40 + 2^38 - 2^36 - 2^25 - 2^23 + 2^21 + 2^19 + 2^17 + 2^15 + 2^10 + 2^8 + 2^6 + 2^4 + 2^2 - 1"
"r2": 3080025
"r2_hex": "0x2eff59"
"r2_bit": "2^22 - 2^20 - 2^16 - 2^7 - 2^5 - 2^3 + 1"
"znprimroot": 6
- "n": 281474976710089
"n_hex": "0xfffffffffdc9"
"n_bit": "2^48 - 2^9 - 2^6 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 7 * 23 * 47 * 4547 * 113621 + 1"
"nd": 249703550768007
"nd_hex": "0xe31aa3715387"
"nd_bit": "2^48 - 2^45 + 2^42 - 2^40 + 2^37 - 2^35 + 2^33 + 2^31 + 2^29 + 2^26 - 2^23 - 2^20 + 2^16 + 2^14 + 2^12 + 2^10 - 2^7 + 2^3 - 1"
"r2": 321489
"r2_hex": "0x4e7d1"
"r2_bit": "2^18 + 2^16 - 2^13 + 2^11 - 2^6 + 2^4 + 1"
"znprimroot": 11
- "n": 281474976708361
"n_hex": "0xfffffffff709"
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"r2_hex": "0x3e8f3d1920ee"
"r2_bit": "2^46 - 2^41 + 2^39 + 2^36 - 2^32 + 2^30 - 2^26 + 2^24 + 2^21 - 2^19 + 2^16 + 2^13 + 2^8 - 2^4 - 2"
"znprimroot": 13
- "n": 281068028559361
"n_hex": "0xffa140000001"
"n_bit": "2^48 - 2^39 + 2^37 + 2^32 + 2^30 + 1"
"n_fac": "2^30 * 3^3 * 5 * 7 * 277 + 1"
"nd": 281068028559359
"nd_hex": "0xffa13fffffff"
"nd_bit": "2^48 - 2^39 + 2^37 + 2^32 + 2^30 - 1"
"r2": 177500745461874
"r2_hex": "0xa16f9ce17072"
"r2_bit": "2^47 + 2^45 + 2^41 - 2^39 - 2^36 - 2^31 + 2^29 - 2^26 + 2^24 - 2^21 + 2^17 - 2^15 - 2^12 + 2^7 - 2^4 + 2"
"znprimroot": 11
- "n": 281451354390529
"n_hex": "0xfffa80000001"
"n_bit": "2^48 - 2^35 + 2^33 + 2^31 + 1"
"n_fac": "2^31 * 3 * 7 * 79^2 + 1"
"nd": 281451354390527
"nd_hex": "0xfffa7fffffff"
"nd_bit": "2^48 - 2^35 + 2^33 + 2^31 - 1"
"r2": 109427174784859
"r2_hex": "0x6385ffe1bf5b"
"r2_bit": "2^47 - 2^45 + 2^42 - 2^39 + 2^35 - 2^33 - 2^21 + 2^17 - 2^14 - 2^7 - 2^5 - 2^2 - 1"
"znprimroot": 23
- "n": 281245195960321
"n_hex": "0xffca80000001"
"n_bit": "2^48 - 2^38 + 2^35 + 2^33 + 2^31 + 1"
"n_fac": "2^31 * 3 * 5 * 8731 + 1"
"nd": 281245195960319
"nd_hex": "0xffca7fffffff"
"nd_bit": "2^48 - 2^38 + 2^35 + 2^33 + 2^31 - 1"
"r2": 135770170943834
"r2_hex": "0x7b7b74cf695a"
"r2_bit": "2^47 - 2^42 - 2^39 - 2^34 - 2^31 - 2^28 + 2^26 + 2^24 - 2^22 + 2^20 - 2^15 - 2^13 + 2^11 + 2^9 - 2^7 - 2^5 - 2^3 + 2"
"znprimroot": 7
- "n": 280278828318721
"n_hex": "0xfee980000001"
"n_bit": "2^48 - 2^40 - 2^37 + 2^35 + 2^33 - 2^31 + 1"
"n_fac": "2^31 * 3 * 5 * 7 * 11 * 113 + 1"
"nd": 280278828318719
"nd_hex": "0xfee97fffffff"
"nd_bit": "2^48 - 2^40 - 2^37 + 2^35 + 2^33 - 2^31 - 1"
"r2": 213461212249256
"r2_hex": "0xc2244fbabca8"
"r2_bit": "2^48 - 2^46 + 2^41 + 2^37 + 2^34 + 2^30 + 2^28 - 2^22 - 2^18 - 2^16 - 2^14 - 2^10 + 2^7 + 2^5 + 2^3"
"znprimroot": 19
- "n": 278023970488321
"n_hex": "0xfcdc80000001"
"n_bit": "2^48 - 2^42 + 2^40 - 2^37 - 2^34 + 2^31 + 1"
"n_fac": "2^31 * 3^3 * 5 * 7 * 137 + 1"
"nd": 278023970488319
"nd_hex": "0xfcdc7fffffff"
"nd_bit": "2^48 - 2^42 + 2^40 - 2^37 - 2^34 + 2^31 - 1"
"r2": 46564001579646
"r2_hex": "0x2a5986c6027e"
"r2_bit": "2^45 + 2^43 + 2^41 + 2^39 - 2^37 - 2^35 + 2^33 - 2^31 + 2^27 - 2^24 - 2^22 + 2^19 - 2^17 + 2^9 + 2^7 - 2"
"znprimroot": 17
- "n": 281212983705601
"n_hex": "0xffc300000001"
"n_bit": "2^48 - 2^38 + 2^34 - 2^32 + 1"
"n_fac": "2^32 * 3^3 * 5^2 * 97 + 1"
"nd": 281212983705599
"nd_hex": "0xffc2ffffffff"
"nd_bit": "2^48 - 2^38 + 2^34 - 2^32 - 1"
"r2": 130970488637577
"r2_hex": "0x771df1738889"
"r2_bit": "2^47 - 2^43 - 2^40 + 2^37 - 2^33 - 2^28 + 2^25 - 2^23 - 2^20 + 2^18 - 2^15 + 2^11 + 2^7 + 2^3 + 1"
"znprimroot": 11
- "n": 281346127691777
"n_hex": "0xffe200000001"
"n_bit": "2^48 - 2^37 + 2^33 + 1"
"n_fac": "2^33 * 7 * 4679 + 1"
"nd": 281346127691775
"nd_hex": "0xffe1ffffffff"
"nd_bit": "2^48 - 2^37 + 2^33 - 1"
"r2": 102512220411517
"r2_hex": "0x5d3bfc7b967d"
"r2_bit": "2^47 - 2^45 - 2^42 + 2^40 + 2^38 - 2^34 - 2^26 + 2^23 - 2^18 - 2^15 + 2^13 - 2^11 - 2^9 + 2^7 - 2^2 + 1"
"znprimroot": 3
- "n": 281019710177281
"n_hex": "0xff9600000001"
"n_bit": "2^48 - 2^39 + 2^37 - 2^35 - 2^33 + 1"
"n_fac": "2^33 * 3^2 * 5 * 727 + 1"
"nd": 281019710177279
"nd_hex": "0xff95ffffffff"
"nd_bit": "2^48 - 2^39 + 2^37 - 2^35 - 2^33 - 1"
"r2": 141793312754704
"r2_hex": "0x80f5d409cc10"
"r2_bit": "2^47 + 2^40 - 2^35 - 2^33 - 2^30 + 2^28 + 2^26 + 2^19 + 2^17 - 2^14 + 2^12 - 2^10 + 2^4"
"znprimroot": 23
- "n": 279396212539393
"n_hex": "0xfe1c00000001"
"n_bit": "2^48 - 2^41 + 2^37 - 2^34 + 1"
"n_fac": "2^34 * 3^2 * 13 * 139 + 1"
"nd": 279396212539391
"nd_hex": "0xfe1bffffffff"
"nd_bit": "2^48 - 2^41 + 2^37 - 2^34 - 1"
"r2": 94387914741392
"r2_hex": "0x55d866211690"
"r2_bit": "2^47 - 2^45 - 2^43 - 2^41 - 2^37 - 2^35 + 2^31 - 2^29 + 2^27 - 2^25 + 2^21 + 2^16 + 2^13 - 2^11 - 2^9 + 2^7 + 2^4"
"znprimroot": 7
- "n": 272386825912321
"n_hex": "0xf7bc00000001"
"n_bit": "2^48 - 2^43 - 2^38 - 2^34 + 1"
"n_fac": "2^34 * 3 * 5 * 7 * 151 + 1"
"nd": 272386825912319
"nd_hex": "0xf7bbffffffff"
"nd_bit": "2^48 - 2^43 - 2^38 - 2^34 - 1"
"r2": 253976018830398
"r2_hex": "0xe6fd6662443e"
"r2_bit": "2^48 - 2^45 + 2^43 - 2^40 - 2^33 - 2^31 - 2^29 + 2^27 - 2^25 + 2^23 - 2^21 + 2^17 + 2^14 + 2^10 + 2^6 - 2"
"znprimroot": 17
- "n": 254347963269121
"n_hex": "0xe75400000001"
"n_bit": "2^48 - 2^45 + 2^43 - 2^40 + 2^38 + 2^36 + 2^34 + 1"
"n_fac": "2^34 * 3^2 * 5 * 7 * 47 + 1"
"nd": 254347963269119
"nd_hex": "0xe753ffffffff"
"nd_bit": "2^48 - 2^45 + 2^43 - 2^40 + 2^38 + 2^36 + 2^34 - 1"
"r2": 191857815426855
"r2_hex": "0xae7e60ef9727"
"r2_bit": "2^48 - 2^46 - 2^44 - 2^41 + 2^39 - 2^33 + 2^31 - 2^29 + 2^24 - 2^20 - 2^15 + 2^13 - 2^11 - 2^8 + 2^5 + 2^3 - 1"
"znprimroot": 26
- "n": 280684702728193
"n_hex": "0xff4800000001"
"n_bit": "2^48 - 2^40 + 2^38 + 2^35 + 1"
"n_fac": "2^35 * 3 * 7 * 389 + 1"
"nd": 280684702728191
"nd_hex": "0xff47ffffffff"
"nd_bit": "2^48 - 2^40 + 2^38 + 2^35 - 1"
"r2": 84350932659582
"r2_hex": "0x4cb77b60ad7e"
"r2_bit": "2^46 + 2^44 - 2^42 + 2^40 - 2^38 - 2^35 - 2^31 - 2^26 - 2^23 - 2^21 + 2^16 - 2^14 - 2^12 - 2^9 - 2^7 - 2"
"znprimroot": 15
- "n": 278004643135489
"n_hex": "0xfcd800000001"
"n_bit": "2^48 - 2^42 + 2^40 - 2^37 - 2^35 + 1"
"n_fac": "2^35 * 3^2 * 29 * 31 + 1"
"nd": 278004643135487
"nd_hex": "0xfcd7ffffffff"
"nd_bit": "2^48 - 2^42 + 2^40 - 2^37 - 2^35 - 1"
"r2": 194398439230336
"r2_hex": "0xb0cde9ea4b80"
"r2_bit": "2^48 - 2^46 - 2^44 + 2^40 - 2^38 + 2^36 - 2^33 - 2^29 + 2^27 + 2^25 - 2^21 + 2^19 + 2^17 + 2^14 + 2^12 - 2^10 - 2^7"
"znprimroot": 11
- "n": 274706108252161
"n_hex": "0xf9d800000001"
"n_bit": "2^48 - 2^43 + 2^41 - 2^37 - 2^35 + 1"
"n_fac": "2^35 * 3 * 5 * 13 * 41 + 1"
"nd": 274706108252159
"nd_hex": "0xf9d7ffffffff"
"nd_bit": "2^48 - 2^43 + 2^41 - 2^37 - 2^35 - 1"
"r2": 261070303183848
"r2_hex": "0xed712aaec3e8"
"r2_bit": "2^48 - 2^44 - 2^41 - 2^39 - 2^36 + 2^32 + 2^30 - 2^28 - 2^26 - 2^24 - 2^22 - 2^20 - 2^16 - 2^14 + 2^10 - 2^5 + 2^3"
"znprimroot": 7
- "n": 273984553746433
"n_hex": "0xf93000000001"
"n_bit": "2^48 - 2^43 + 2^40 + 2^38 - 2^36 + 1"
"n_fac": "2^36 * 3^2 * 443 + 1"
"nd": 273984553746431
"nd_hex": "0xf92fffffffff"
"nd_bit": "2^48 - 2^43 + 2^40 + 2^38 - 2^36 - 1"
"r2": 250208993666643
"r2_hex": "0xe390522fe653"
"r2_bit": "2^48 - 2^45 + 2^42 - 2^39 + 2^36 + 2^30 + 2^28 + 2^25 + 2^22 - 2^20 - 2^13 + 2^11 - 2^9 + 2^6 + 2^4 + 2^2 - 1"
"znprimroot": 7
- "n": 266975167119361
"n_hex": "0xf2d000000001"
"n_bit": "2^48 - 2^44 + 2^42 - 2^40 - 2^38 + 2^36 + 1"
"n_fac": "2^36 * 3 * 5 * 7 * 37 + 1"
"nd": 266975167119359
"nd_hex": "0xf2cfffffffff"
"nd_bit": "2^48 - 2^44 + 2^42 - 2^40 - 2^38 + 2^36 - 1"
"r2": 92945860521763
"r2_hex": "0x5488a4ffef23"
"r2_bit": "2^46 + 2^44 + 2^42 + 2^39 + 2^35 + 2^31 + 2^29 + 2^26 + 2^24 - 2^12 - 2^8 + 2^5 + 2^2 - 1"
"znprimroot": 31
- "n": 194819716546561
"n_hex": "0xb13000000001"
"n_bit": "2^48 - 2^46 - 2^44 + 2^40 + 2^38 - 2^36 + 1"
"n_fac": "2^36 * 3^4 * 5 * 7 + 1"
"nd": 194819716546559
"nd_hex": "0xb12fffffffff"
"nd_bit": "2^48 - 2^46 - 2^44 + 2^40 + 2^38 - 2^36 - 1"
"r2": 26327170847631
"r2_hex": "0x17f1c5aa938f"
"r2_bit": "2^45 - 2^43 - 2^36 + 2^33 - 2^30 + 2^27 - 2^25 - 2^23 + 2^21 + 2^19 + 2^17 + 2^15 + 2^12 + 2^10 - 2^7 + 2^4 - 1"
"znprimroot": 22
- "n": 280238026129409
"n_hex": "0xfee000000001"
"n_bit": "2^48 - 2^40 - 2^37 + 1"
"n_fac": "2^37 * 2039 + 1"
"nd": 280238026129407
"nd_hex": "0xfedfffffffff"
"nd_bit": "2^48 - 2^40 - 2^37 - 1"
"r2": 97438758200354
"r2_hex": "0x589eba91e422"
"r2_bit": "2^47 - 2^45 - 2^43 + 2^39 + 2^37 - 2^32 - 2^30 - 2^27 + 2^25 + 2^23 + 2^20 + 2^17 - 2^13 + 2^10 + 2^5 + 2"
"znprimroot": 3
- "n": 28862180229121
"n_hex": "0x1a4000000001"
"n_bit": "2^45 - 2^43 + 2^41 + 2^38 + 1"
"n_fac": "2^38 * 3 * 5 * 7 + 1"
"nd": 28862180229119
"nd_hex": "0x1a3fffffffff"
"nd_bit": "2^45 - 2^43 + 2^41 + 2^38 - 1"
"r2": 18571274970198
"r2_hex": "0x10e3f63f6456"
"r2_bit": "2^44 + 2^40 - 2^37 + 2^34 - 2^27 - 2^25 + 2^22 - 2^15 - 2^13 + 2^10 + 2^7 - 2^5 - 2^3 - 2"
"znprimroot": 19
- "n": 279825709268993
"n_hex": "0xfe8000000001"
"n_bit": "2^48 - 2^41 + 2^39 + 1"
"n_fac": "2^39 * 509 + 1"
"nd": 279825709268991
"nd_hex": "0xfe7fffffffff"
"nd_bit": "2^48 - 2^41 + 2^39 - 1"
"r2": 124784849119326
"r2_hex": "0x717dbc9ae85e"
"r2_bit": "2^47 - 2^44 + 2^41 - 2^39 - 2^33 - 2^30 - 2^26 + 2^23 + 2^21 - 2^18 - 2^16 - 2^13 + 2^11 + 2^7 - 2^5 - 2"
"znprimroot": 3
- "n": 272129127874561
"n_hex": "0xf78000000001"
"n_bit": "2^48 - 2^43 - 2^39 + 1"
"n_fac": "2^39 * 3^2 * 5 * 11 + 1"
"nd": 272129127874559
"nd_hex": "0xf77fffffffff"
"nd_bit": "2^48 - 2^43 - 2^39 - 1"
"r2": 15072194242979
"r2_hex": "0xdb544c8a9a3"
"r2_bit": "2^44 - 2^41 - 2^38 - 2^36 + 2^34 + 2^32 + 2^30 + 2^26 + 2^24 - 2^22 + 2^19 + 2^15 + 2^13 + 2^11 + 2^9 - 2^7 + 2^5 + 2^2 - 1"
"znprimroot": 14
- "n": 217703302299649
"n_hex": "0xc60000000001"
"n_bit": "2^48 - 2^46 + 2^43 - 2^41 + 1"
"n_fac": "2^41 * 3^2 * 11 + 1"
"nd": 217703302299647
"nd_hex": "0xc5ffffffffff"
"nd_bit": "2^48 - 2^46 + 2^43 - 2^41 - 1"
"r2": 214415873594381
"r2_hex": "0xc30295fad40d"
"r2_bit": "2^48 - 2^46 + 2^42 - 2^40 + 2^33 + 2^31 + 2^29 - 2^27 - 2^25 - 2^18 - 2^16 - 2^14 + 2^12 + 2^10 + 2^4 - 2^2 + 1"
"znprimroot": 7
- "n": 79164837199873
"n_hex": "0x480000000001"
"n_bit": "2^46 + 2^43 + 1"
"n_fac": "2^43 * 3^2 + 1"
"nd": 79164837199871
"nd_hex": "0x47ffffffffff"
"nd_bit": "2^46 + 2^43 - 1"
"r2": 72323431515946
"r2_hex": "0x41c71c71c72a"
"r2_bit": "2^46 + 2^41 - 2^38 + 2^35 - 2^32 + 2^29 - 2^26 + 2^23 - 2^20 + 2^17 - 2^14 + 2^11 - 2^8 + 2^5 + 2^3 + 2"
"znprimroot": 5
- "n": 263882790666241
"n_hex": "0xf00000000001"
"n_bit": "2^48 - 2^44 + 1"
"n_fac": "2^44 * 3 * 5 + 1"
"nd": 263882790666239
"nd_hex": "0xefffffffffff"
"nd_bit": "2^48 - 2^44 - 1"
"r2": 245117792218865
"r2_hex": "0xdeeeeeeeeef1"
"r2_bit": "2^48 - 2^45 - 2^40 - 2^36 - 2^32 - 2^28 - 2^24 - 2^20 - 2^16 - 2^12 - 2^8 - 2^4 + 1"
"znprimroot": 7
Raw
result_prime_0049.yaml
- "r": 49
"primes":
- "n": 562949953421231
"n_hex": "0x1ffffffffffaf"
"n_bit": "2^49 - 2^6 - 2^4 - 1"
"n_fac": "2 * 5 * 223 * 252443925301 + 1"
"nd": 340549971822769
"nd_hex": "0x135ba781948b1"
"nd_bit": "2^48 + 2^46 - 2^43 - 2^41 - 2^38 - 2^35 + 2^33 + 2^31 - 2^27 + 2^21 - 2^19 + 2^16 + 2^14 + 2^11 + 2^8 - 2^6 - 2^4 + 1"
"r2": 6561
"r2_hex": "0x19a1"
"r2_bit": "2^13 - 2^11 + 2^9 - 2^7 + 2^5 + 1"
"znprimroot": 17
- "n": 562949953421131
"n_hex": "0x1ffffffffff4b"
"n_bit": "2^49 - 2^8 + 2^6 + 2^4 - 2^2 - 1"
"n_fac": "2 * 3^2 * 5 * 11 * 568636316587 + 1"
"nd": 242597217496477
"nd_hex": "0xdca410f8ed9d"
"nd_bit": "2^48 - 2^45 - 2^42 + 2^39 + 2^37 + 2^34 + 2^28 + 2^24 - 2^19 + 2^16 - 2^12 - 2^9 - 2^7 + 2^5 - 2^2 + 1"
"r2": 32761
"r2_hex": "0x7ff9"
"r2_bit": "2^15 - 2^3 + 1"
"znprimroot": 2
- "n": 562949953419211
"n_hex": "0x1fffffffff7cb"
"n_bit": "2^49 - 2^11 - 2^6 + 2^4 - 2^2 - 1"
"n_fac": "2 * 3 * 5 * 7 * 23 * 116552785387 + 1"
"nd": 323676127431197
"nd_hex": "0x12661b8990a1d"
"nd_bit": "2^48 + 2^45 + 2^43 - 2^41 + 2^39 - 2^37 + 2^33 - 2^30 - 2^27 + 2^23 + 2^21 - 2^19 + 2^16 + 2^11 + 2^9 + 2^5 - 2^2 + 1"
"r2": 4414201
"r2_hex": "0x435af9"
"r2_bit": "2^22 + 2^18 - 2^15 - 2^13 - 2^10 - 2^8 - 2^3 + 1"
"znprimroot": 3
- "n": 562949953421173
"n_hex": "0x1ffffffffff75"
"n_bit": "2^49 - 2^7 - 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3 * 31 * 1093 * 2861 * 483937 + 1"
"nd": 400949966825251
"nd_hex": "0x16ca970586723"
"nd_bit": "2^49 - 2^47 - 2^44 - 2^42 + 2^39 + 2^37 + 2^35 + 2^33 - 2^31 - 2^28 + 2^23 - 2^21 - 2^19 + 2^15 - 2^13 + 2^11 - 2^8 + 2^5 + 2^2 - 1"
"r2": 19321
"r2_hex": "0x4b79"
"r2_bit": "2^14 + 2^12 - 2^10 - 2^7 - 2^3 + 1"
"znprimroot": 2
- "n": 562949953420741
"n_hex": "0x1fffffffffdc5"
"n_bit": "2^49 - 2^9 - 2^6 + 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 47 * 199627643057 + 1"
"nd": 252390872286963
"nd_hex": "0xe58c544986f3"
"nd_bit": "2^48 - 2^45 + 2^43 - 2^41 - 2^39 + 2^36 - 2^34 + 2^30 + 2^28 + 2^26 + 2^22 + 2^19 + 2^17 - 2^15 + 2^11 - 2^8 - 2^4 + 2^2 - 1"
"r2": 326041
"r2_hex": "0x4f999"
"r2_bit": "2^18 + 2^16 - 2^11 + 2^9 - 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 562949953421201
"n_hex": "0x1ffffffffff91"
"n_bit": "2^49 - 2^7 + 2^4 + 1"
"n_fac": "2^4 * 5^2 * 137 * 10272809369 + 1"
"nd": 537591847411343
"nd_hex": "0x1e8efdb195e8f"
"nd_bit": "2^49 - 2^45 + 2^43 + 2^40 - 2^36 - 2^29 - 2^26 - 2^24 + 2^21 - 2^19 + 2^17 - 2^15 - 2^13 - 2^9 + 2^7 + 2^4 - 1"
"r2": 12321
"r2_hex": "0x3021"
"r2_bit": "2^14 - 2^12 + 2^5 + 1"
"znprimroot": 3
- "n": 562949953418161
"n_hex": "0x1fffffffff3b1"
"n_bit": "2^49 - 2^12 + 2^10 - 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5 * 7 * 11 * 1171 * 8671409 + 1"
"nd": 148821742684847
"nd_hex": "0x875a431b8aaf"
"nd_bit": "2^47 + 2^43 - 2^39 - 2^37 - 2^35 + 2^33 + 2^30 + 2^26 - 2^24 + 2^21 - 2^18 - 2^15 + 2^12 - 2^10 - 2^8 - 2^6 - 2^4 - 1"
"r2": 9928801
"r2_hex": "0x978061"
"r2_bit": "2^23 + 2^21 - 2^19 - 2^15 + 2^7 - 2^5 + 1"
"znprimroot": 29
- "n": 562949953418401
"n_hex": "0x1fffffffff4a1"
"n_bit": "2^49 - 2^12 + 2^10 + 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3 * 5^2 * 97 * 2418169903 + 1"
"nd": 63817754939551
"nd_hex": "0x3a0aba9d109f"
"nd_bit": "2^46 - 2^43 + 2^41 + 2^36 - 2^34 - 2^32 - 2^30 - 2^27 + 2^25 + 2^23 + 2^21 - 2^18 + 2^16 + 2^12 + 2^7 + 2^5 - 1"
"r2": 8473921
"r2_hex": "0x814d41"
"r2_bit": "2^23 + 2^16 + 2^14 + 2^12 - 2^10 + 2^8 + 2^6 + 1"
"znprimroot": 11
- "n": 562949953417441
"n_hex": "0x1fffffffff0e1"
"n_bit": "2^49 - 2^12 + 2^8 - 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5 * 107 * 1217873731c + 1"
"nd": 524702514064607
"nd_hex": "0x1dd36d2f6acdf"
"nd_bit": "2^49 - 2^45 - 2^42 + 2^40 + 2^38 - 2^35 - 2^32 - 2^30 + 2^28 + 2^26 - 2^24 - 2^19 - 2^16 - 2^14 - 2^12 - 2^10 + 2^8 - 2^5 - 1"
"r2": 14984641
"r2_hex": "0xe4a5c1"
"r2_bit": "2^24 - 2^21 + 2^18 + 2^15 + 2^13 + 2^11 - 2^9 - 2^6 + 1"
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"znprimroot": 11
- "n": 562940558180353
"n_hex": "0x1fffdd0000001"
"n_bit": "2^49 - 2^33 - 2^30 + 2^28 + 1"
"n_fac": "2^28 * 3^3 * 11 * 23 * 307 + 1"
"nd": 562940558180351
"nd_hex": "0x1fffdcfffffff"
"nd_bit": "2^49 - 2^33 - 2^30 + 2^28 - 1"
"r2": 347273875528575
"r2_hex": "0x13bd7fffd9b7f"
"r2_bit": "2^48 + 2^46 - 2^42 - 2^37 - 2^35 - 2^17 - 2^15 + 2^13 - 2^10 - 2^7 - 1"
"znprimroot": 10
- "n": 562389728624641
"n_hex": "0x1ff7d90000001"
"n_bit": "2^49 - 2^39 - 2^33 - 2^31 + 2^28 + 1"
"n_fac": "2^28 * 3^4 * 5 * 7 * 739 + 1"
"nd": 562389728624639
"nd_hex": "0x1ff7d8fffffff"
"nd_bit": "2^49 - 2^39 - 2^33 - 2^31 + 2^28 - 1"
"r2": 377800871415323
"r2_hex": "0x1579b9ebc8e1b"
"r2_bit": "2^49 - 2^47 - 2^45 - 2^43 - 2^39 + 2^37 - 2^34 - 2^31 + 2^29 - 2^24 - 2^22 - 2^18 + 2^15 + 2^12 - 2^9 + 2^5 - 2^2 - 1"
"znprimroot": 26
- "n": 562756143022081
"n_hex": "0x1ffd2e0000001"
"n_bit": "2^49 - 2^38 + 2^36 + 2^34 - 2^32 - 2^29 + 1"
"n_fac": "2^29 * 3 * 5 * 7 * 67 * 149 + 1"
"nd": 562756143022079
"nd_hex": "0x1ffd2dfffffff"
"nd_bit": "2^49 - 2^38 + 2^36 + 2^34 - 2^32 - 2^29 - 1"
"r2": 299501424575550
"r2_hex": "0x110651c05843e"
"r2_bit": "2^48 + 2^44 + 2^39 - 2^37 + 2^34 + 2^32 + 2^29 - 2^26 + 2^19 - 2^17 - 2^15 + 2^10 + 2^6 - 2"
"znprimroot": 11
- "n": 558922884710401
"n_hex": "0x1fc5660000001"
"n_bit": "2^49 - 2^42 + 2^39 - 2^37 - 2^35 - 2^33 + 2^31 - 2^29 + 1"
"n_fac": "2^29 * 3^2 * 5^2 * 7 * 661 + 1"
"nd": 558922884710399
"nd_hex": "0x1fc565fffffff"
"nd_bit": "2^49 - 2^42 + 2^39 - 2^37 - 2^35 - 2^33 + 2^31 - 2^29 - 1"
"r2": 339721688354160
"r2_hex": "0x134f99e8e8d70"
"r2_bit": "2^48 + 2^46 - 2^44 + 2^42 + 2^40 - 2^35 + 2^33 - 2^31 + 2^29 - 2^25 + 2^23 + 2^20 - 2^17 + 2^15 + 2^12 - 2^9 - 2^7 - 2^4"
"znprimroot": 17
- "n": 562948879679489
"n_hex": "0x1ffffc0000001"
"n_bit": "2^49 - 2^30 + 1"
"n_fac": "2^30 * 524287 + 1"
"nd": 562948879679487
"nd_hex": "0x1ffffbfffffff"
"nd_bit": "2^49 - 2^30 - 1"
"r2": 2196875769857
"r2_hex": "0x1ff7ffff801"
"r2_bit": "2^41 - 2^31 - 2^11 + 1"
"znprimroot": 3
- "n": 562860832849921
"n_hex": "0x1ffeb40000001"
"n_bit": "2^49 - 2^36 - 2^34 - 2^32 + 2^30 + 1"
"n_fac": "2^30 * 3^3 * 5 * 11 * 353 + 1"
"nd": 562860832849919
"nd_hex": "0x1ffeb3fffffff"
"nd_bit": "2^49 - 2^36 - 2^34 - 2^32 + 2^30 - 1"
"r2": 504492213186376
"r2_hex": "0x1cad53f28af48"
"r2_bit": "2^49 - 2^46 + 2^44 - 2^42 - 2^40 - 2^38 + 2^36 + 2^34 + 2^32 + 2^30 - 2^24 + 2^21 + 2^19 + 2^16 - 2^14 - 2^12 - 2^8 + 2^6 + 2^3"
"znprimroot": 23
- "n": 558415541698561
"n_hex": "0x1fbe040000001"
"n_bit": "2^49 - 2^42 - 2^37 + 2^30 + 1"
"n_fac": "2^30 * 3^2 * 5 * 7 * 13 * 127 + 1"
"nd": 558415541698559
"nd_hex": "0x1fbe03fffffff"
"nd_bit": "2^49 - 2^42 - 2^37 + 2^30 - 1"
"r2": 373705865336106
"r2_hex": "0x153e22d5a952a"
"r2_bit": "2^48 + 2^46 + 2^44 + 2^42 - 2^37 + 2^33 + 2^30 - 2^28 - 2^25 - 2^23 - 2^21 - 2^19 + 2^17 + 2^15 + 2^12 + 2^10 + 2^8 + 2^5 + 2^3 + 2"
"znprimroot": 23
- "n": 561942783590401
"n_hex": "0x1ff1580000001"
"n_bit": "2^49 - 2^40 + 2^37 - 2^35 - 2^33 - 2^31 + 1"
"n_fac": "2^31 * 3^2 * 5^2 * 1163 + 1"
"nd": 561942783590399
"nd_hex": "0x1ff157fffffff"
"nd_bit": "2^49 - 2^40 + 2^37 - 2^35 - 2^33 - 2^31 - 1"
"r2": 238401092032628
"r2_hex": "0xd8d314679874"
"r2_bit": "2^48 - 2^45 - 2^43 + 2^40 - 2^38 + 2^36 + 2^34 - 2^32 + 2^28 + 2^26 + 2^23 - 2^21 + 2^19 - 2^15 + 2^13 - 2^11 + 2^7 - 2^4 + 2^2"
"znprimroot": 7
- "n": 562361542901761
"n_hex": "0x1ff7700000001"
"n_bit": "2^49 - 2^39 - 2^35 - 2^32 + 1"
"n_fac": "2^32 * 3 * 5 * 7 * 29 * 43 + 1"
"nd": 562361542901759
"nd_hex": "0x1ff76ffffffff"
"nd_bit": "2^49 - 2^39 - 2^35 - 2^32 - 1"
"r2": 485244789435979
"r2_hex": "0x1b953db4dae4b"
"r2_bit": "2^49 - 2^46 - 2^43 + 2^40 + 2^38 + 2^36 + 2^34 - 2^29 - 2^26 - 2^24 + 2^22 + 2^20 - 2^17 - 2^14 - 2^12 - 2^9 + 2^6 + 2^4 - 2^2 - 1"
"znprimroot": 38
- "n": 562310003294209
"n_hex": "0x1ff6b00000001"
"n_bit": "2^49 - 2^39 - 2^36 - 2^34 - 2^32 + 1"
"n_fac": "2^32 * 3^3 * 13 * 373 + 1"
"nd": 562310003294207
"nd_hex": "0x1ff6affffffff"
"nd_bit": "2^49 - 2^39 - 2^36 - 2^34 - 2^32 - 1"
"r2": 236179523296745
"r2_hex": "0xd6cdd496dde9"
"r2_bit": "2^48 - 2^45 - 2^43 - 2^40 - 2^38 + 2^36 - 2^33 - 2^30 + 2^28 + 2^26 + 2^23 + 2^21 - 2^19 - 2^16 - 2^13 - 2^9 - 2^5 + 2^3 + 1"
"znprimroot": 19
- "n": 561846146826241
"n_hex": "0x1feff00000001"
"n_bit": "2^49 - 2^40 - 2^32 + 1"
"n_fac": "2^32 * 3^4 * 5 * 17 * 19 + 1"
"nd": 561846146826239
"nd_hex": "0x1fefeffffffff"
"nd_bit": "2^49 - 2^40 - 2^32 - 1"
"r2": 193851180359344
"r2_hex": "0xb04e7ebe9eb0"
"r2_bit": "2^48 - 2^46 - 2^44 + 2^38 + 2^36 - 2^33 + 2^31 - 2^24 - 2^22 - 2^17 + 2^15 + 2^13 - 2^8 - 2^6 - 2^4"
"znprimroot": 11
- "n": 562941363486721
"n_hex": "0x1fffe00000001"
"n_bit": "2^49 - 2^33 + 1"
"n_fac": "2^33 * 3 * 5 * 17 * 257 + 1"
"nd": 562941363486719
"nd_hex": "0x1fffdffffffff"
"nd_bit": "2^49 - 2^33 - 1"
"r2": 562941363355648
"r2_hex": "0x1fffdfffe0000"
"r2_bit": "2^49 - 2^33 - 2^17"
"znprimroot": 13
- "n": 562932773552129
"n_hex": "0x1fffc00000001"
"n_bit": "2^49 - 2^34 + 1"
"n_fac": "2^34 * 7 * 31 * 151 + 1"
"nd": 562932773552127
"nd_hex": "0x1fffbffffffff"
"nd_bit": "2^49 - 2^34 - 1"
"r2": 240517644273
"r2_hex": "0x37fff7fff1"
"r2_bit": "2^38 - 2^35 - 2^19 - 2^4 + 1"
"znprimroot": 3
- "n": 562451737214977
"n_hex": "0x1ff8c00000001"
"n_bit": "2^49 - 2^39 + 2^36 - 2^34 + 1"
"n_fac": "2^34 * 3 * 7 * 1559 + 1"
"nd": 562451737214975
"nd_hex": "0x1ff8bffffffff"
"nd_bit": "2^49 - 2^39 + 2^36 - 2^34 - 1"
"r2": 369074688363096
"r2_hex": "0x14fabe5b20a58"
"r2_bit": "2^48 + 2^46 + 2^44 - 2^38 - 2^36 - 2^34 - 2^29 + 2^27 - 2^25 - 2^22 - 2^20 + 2^17 + 2^11 + 2^9 + 2^7 - 2^5 - 2^3"
"znprimroot": 5
- "n": 561008628203521
"n_hex": "0x1fe3c00000001"
"n_bit": "2^49 - 2^41 + 2^38 - 2^34 + 1"
"n_fac": "2^34 * 3 * 5 * 7 * 311 + 1"
"nd": 561008628203519
"nd_hex": "0x1fe3bffffffff"
"nd_bit": "2^49 - 2^41 + 2^38 - 2^34 - 1"
"r2": 256145131733729
"r2_hex": "0xe8f66f9682e1"
"r2_bit": "2^48 - 2^45 + 2^43 + 2^40 - 2^35 - 2^33 + 2^31 - 2^28 - 2^23 + 2^21 - 2^19 - 2^17 + 2^15 + 2^10 - 2^8 - 2^5 + 1"
"znprimroot": 51
- "n": 561266326241281
"n_hex": "0x1fe7800000001"
"n_bit": "2^49 - 2^41 + 2^39 - 2^35 + 1"
"n_fac": "2^35 * 3^3 * 5 * 11^2 + 1"
"nd": 561266326241279
"nd_hex": "0x1fe77ffffffff"
"nd_bit": "2^49 - 2^41 + 2^39 - 2^35 - 1"
"r2": 337063983023885
"r2_hex": "0x1328ed2f9870d"
"r2_bit": "2^48 + 2^46 - 2^44 + 2^41 + 2^39 + 2^36 - 2^32 - 2^30 + 2^28 + 2^26 - 2^24 - 2^19 + 2^17 - 2^15 + 2^11 - 2^8 + 2^4 - 2^2 + 1"
"znprimroot": 7
- "n": 562194039177217
"n_hex": "0x1ff5000000001"
"n_bit": "2^49 - 2^40 + 2^38 + 2^36 + 1"
"n_fac": "2^36 * 3^4 * 101 + 1"
"nd": 562194039177215
"nd_hex": "0x1ff4fffffffff"
"nd_bit": "2^49 - 2^40 + 2^38 + 2^36 - 1"
"r2": 327790887644377
"r2_hex": "0x12a1fc36b2cd9"
"r2_bit": "2^48 + 2^45 + 2^43 + 2^41 + 2^37 - 2^30 + 2^26 - 2^23 - 2^20 - 2^18 - 2^16 + 2^14 - 2^12 - 2^10 + 2^8 - 2^5 - 2^3 + 1"
"znprimroot": 5
- "n": 541165879296001
"n_hex": "0x1ec3000000001"
"n_bit": "2^49 - 2^44 - 2^42 + 2^38 - 2^36 + 1"
"n_fac": "2^36 * 3^2 * 5^3 * 7 + 1"
"nd": 541165879295999
"nd_hex": "0x1ec2fffffffff"
"nd_bit": "2^49 - 2^44 - 2^42 + 2^38 - 2^36 - 1"
"r2": 172296185946439
"r2_hex": "0x9cb3d4f5a147"
"r2_bit": "2^47 + 2^45 - 2^42 + 2^40 - 2^38 - 2^36 + 2^34 - 2^30 + 2^28 + 2^26 + 2^24 - 2^19 - 2^17 - 2^15 + 2^13 + 2^8 + 2^6 + 2^3 - 1"
"znprimroot": 13
- "n": 548381424353281
"n_hex": "0x1f2c000000001"
"n_bit": "2^49 - 2^44 + 2^42 - 2^40 - 2^38 + 1"
"n_fac": "2^38 * 3 * 5 * 7 * 19 + 1"
"nd": 548381424353279
"nd_hex": "0x1f2bfffffffff"
"nd_bit": "2^49 - 2^44 + 2^42 - 2^40 - 2^38 - 1"
"r2": 317096948916008
"r2_hex": "0x12065e2ffdf28"
"r2_bit": "2^48 + 2^45 + 2^39 - 2^37 + 2^35 - 2^33 - 2^29 + 2^26 - 2^24 - 2^13 - 2^8 + 2^5 + 2^3"
"znprimroot": 17
- "n": 531888749936641
"n_hex": "0x1e3c000000001"
"n_bit": "2^49 - 2^45 + 2^42 - 2^38 + 1"
"n_fac": "2^38 * 3^2 * 5 * 43 + 1"
"nd": 531888749936639
"nd_hex": "0x1e3bfffffffff"
"nd_bit": "2^49 - 2^45 + 2^42 - 2^38 - 1"
"r2": 295054229425223
"r2_hex": "0x10c59aa88cc47"
"r2_bit": "2^48 + 2^44 - 2^42 + 2^39 - 2^37 - 2^35 + 2^33 - 2^31 + 2^29 + 2^27 + 2^25 + 2^23 + 2^19 + 2^16 - 2^14 + 2^12 - 2^10 + 2^6 + 2^3 - 1"
"znprimroot": 19
- "n": 559101662724097
"n_hex": "0x1fc8000000001"
"n_bit": "2^49 - 2^42 + 2^39 + 1"
"n_fac": "2^39 * 3^2 * 113 + 1"
"nd": 559101662724095
"nd_hex": "0x1fc7fffffffff"
"nd_bit": "2^49 - 2^42 + 2^39 - 1"
"r2": 183042198281460
"r2_hex": "0xa679d5351cf4"
"r2_bit": "2^47 + 2^45 + 2^43 - 2^41 + 2^39 - 2^35 + 2^33 - 2^30 + 2^28 + 2^26 + 2^24 + 2^22 - 2^20 + 2^18 + 2^16 + 2^13 - 2^10 + 2^8 - 2^4 + 2^2"
"znprimroot": 5
- "n": 519519244124161
"n_hex": "0x1d88000000001"
"n_bit": "2^49 - 2^45 - 2^43 + 2^39 + 1"
"n_fac": "2^39 * 3^3 * 5 * 7 + 1"
"nd": 519519244124159
"nd_hex": "0x1d87fffffffff"
"nd_bit": "2^49 - 2^45 - 2^43 + 2^39 - 1"
"r2": 342715447369045
"r2_hex": "0x137b2a87fdd55"
"r2_bit": "2^48 + 2^46 - 2^43 - 2^38 - 2^36 + 2^33 + 2^31 + 2^29 + 2^27 + 2^23 - 2^13 - 2^10 + 2^8 + 2^6 + 2^4 + 2^2 + 1"
"znprimroot": 26
- "n": 560750930165761
"n_hex": "0x1fe0000000001"
"n_bit": "2^49 - 2^41 + 1"
"n_fac": "2^41 * 3 * 5 * 17 + 1"
"nd": 560750930165759
"nd_hex": "0x1fdffffffffff"
"nd_bit": "2^49 - 2^41 - 1"
"r2": 560742306545152
"r2_hex": "0x1fdfdfdfdfe00"
"r2_bit": "2^49 - 2^41 - 2^33 - 2^25 - 2^17 - 2^9"
"znprimroot": 14
- "n": 505775348776961
"n_hex": "0x1cc0000000001"
"n_bit": "2^49 - 2^46 + 2^44 - 2^42 + 1"
"n_fac": "2^42 * 5 * 23 + 1"
"nd": 505775348776959
"nd_hex": "0x1cbffffffffff"
"nd_bit": "2^49 - 2^46 + 2^44 - 2^42 - 1"
"r2": 191448876822494
"r2_hex": "0xae1f2a4bafde"
"r2_bit": "2^48 - 2^46 - 2^44 - 2^41 + 2^37 - 2^32 + 2^29 + 2^27 + 2^25 + 2^22 + 2^20 - 2^18 - 2^14 - 2^12 - 2^5 - 2"
"znprimroot": 3
- "n": 474989023199233
"n_hex": "0x1b00000000001"
"n_bit": "2^49 - 2^46 - 2^44 + 1"
"n_fac": "2^44 * 3^3 + 1"
"nd": 474989023199231
"nd_hex": "0x1afffffffffff"
"nd_bit": "2^49 - 2^46 - 2^44 - 1"
"r2": 300370287647253
"r2_hex": "0x1112f684bda15"
"r2_bit": "2^48 + 2^44 + 2^40 + 2^38 - 2^36 - 2^31 - 2^29 + 2^27 + 2^22 + 2^20 - 2^18 - 2^13 - 2^11 + 2^9 + 2^4 + 2^2 + 1"
"znprimroot": 5
- "n": 263882790666241
"n_hex": "0xf00000000001"
"n_bit": "2^48 - 2^44 + 1"
"n_fac": "2^44 * 3 * 5 + 1"
"nd": 263882790666239
"nd_hex": "0xefffffffffff"
"nd_bit": "2^48 - 2^44 - 1"
"r2": 188822796876737
"r2_hex": "0xabbbbbbbbbc1"
"r2_bit": "2^48 - 2^46 - 2^44 - 2^42 - 2^38 - 2^34 - 2^30 - 2^26 - 2^22 - 2^18 - 2^14 - 2^10 - 2^6 + 1"
"znprimroot": 7
Raw
result_prime_0050.yaml
- "r": 50
"primes":
- "n": 1125899906842597
"n_hex": "0x3ffffffffffe5"
"n_bit": "2^50 - 2^5 + 2^2 + 1"
"n_fac": "2^2 * 3 * 6637 * 14136656959c + 1"
"nd": 458699962046995
"nd_hex": "0x1a12f684bda13"
"nd_bit": "2^49 - 2^47 + 2^45 + 2^40 + 2^38 - 2^36 - 2^31 - 2^29 + 2^27 + 2^22 + 2^20 - 2^18 - 2^13 - 2^11 + 2^9 + 2^4 + 2^2 - 1"
"r2": 729
"r2_hex": "0x2d9"
"r2_bit": "2^10 - 2^8 - 2^5 - 2^3 + 1"
"znprimroot": 6
- "n": 1125899906841973
"n_hex": "0x3fffffffffd75"
"n_bit": "2^50 - 2^9 - 2^7 - 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 19 * 31 * 59 * 373 * 2412799 + 1"
"nd": 480799038559523
"nd_hex": "0x1b548bfe6d523"
"nd_bit": "2^49 - 2^46 - 2^44 + 2^42 + 2^40 + 2^38 + 2^35 + 2^32 - 2^30 - 2^21 + 2^19 - 2^16 - 2^14 + 2^12 + 2^10 + 2^8 + 2^5 + 2^2 - 1"
"r2": 423801
"r2_hex": "0x67779"
"r2_bit": "2^19 - 2^17 + 2^15 - 2^11 - 2^7 - 2^3 + 1"
"znprimroot": 2
- "n": 1125899906841901
"n_hex": "0x3fffffffffd2d"
"n_bit": "2^50 - 2^10 + 2^8 + 2^6 - 2^4 - 2^2 + 1"
"n_fac": "2^2 * 3^4 * 5^2 * 138999988499c + 1"
"nd": 844035614811483
"nd_hex": "0x2ffa55affa55b"
"nd_bit": "2^50 - 2^48 - 2^39 + 2^37 + 2^35 - 2^33 - 2^31 - 2^29 - 2^26 - 2^24 - 2^15 + 2^13 + 2^11 - 2^9 - 2^7 - 2^5 - 2^2 - 1"
"r2": 522729
"r2_hex": "0x7f9e9"
"r2_bit": "2^19 - 2^11 + 2^9 - 2^5 + 2^3 + 1"
"znprimroot": 2
- "n": 1125899906840101
"n_hex": "0x3fffffffff625"
"n_bit": "2^50 - 2^11 - 2^9 + 2^5 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5^2 * 7 * 101 * 103 * 17179109 + 1"
"nd": 126736255863379
"nd_hex": "0x73441582ca53"
"nd_bit": "2^47 - 2^44 + 2^42 - 2^40 + 2^38 + 2^34 + 2^29 - 2^27 - 2^25 - 2^23 + 2^18 - 2^16 - 2^14 + 2^11 + 2^9 + 2^6 + 2^4 + 2^2 - 1"
"r2": 6365529
"r2_hex": "0x612159"
"r2_bit": "2^23 - 2^21 + 2^16 + 2^13 + 2^9 - 2^7 - 2^5 - 2^3 + 1"
"znprimroot": 6
- "n": 1125899906842553
"n_hex": "0x3ffffffffffb9"
"n_bit": "2^50 - 2^6 - 2^3 + 1"
"n_fac": "2^3 * 17 * 8278675785607 + 1"
"nd": 364728138836343
"nd_hex": "0x14bb7e327a977"
"nd_bit": "2^48 + 2^46 + 2^44 - 2^42 - 2^38 - 2^35 - 2^29 + 2^26 - 2^24 + 2^21 + 2^19 - 2^15 + 2^13 + 2^11 + 2^9 - 2^7 - 2^3 - 1"
"r2": 5041
"r2_hex": "0x13b1"
"r2_bit": "2^12 + 2^10 - 2^6 - 2^4 + 1"
"znprimroot": 3
- "n": 1125899906842201
"n_hex": "0x3fffffffffe59"
"n_bit": "2^50 - 2^9 + 2^7 - 2^5 - 2^3 + 1"
"n_fac": "2^3 * 3 * 5^2 * 7 * 19 * 139 * 101503751 + 1"
"nd": 867714821821975
"nd_hex": "0x3152e99b89617"
"nd_bit": "2^50 - 2^48 + 2^44 + 2^42 + 2^40 + 2^38 - 2^36 - 2^33 + 2^31 + 2^29 - 2^27 + 2^25 - 2^22 - 2^19 + 2^15 + 2^13 - 2^11 - 2^9 + 2^5 - 2^3 - 1"
"r2": 178929
"r2_hex": "0x2baf1"
"r2_bit": "2^18 - 2^16 - 2^14 - 2^10 - 2^8 - 2^4 + 1"
"znprimroot": 22
- "n": 1125899906842273
"n_hex": "0x3fffffffffea1"
"n_bit": "2^50 - 2^9 + 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3 * 263 * 44593627489 + 1"
"nd": 468323038173855
"nd_hex": "0x1a9eff4549a9f"
"nd_bit": "2^49 - 2^47 + 2^45 + 2^43 + 2^41 - 2^36 - 2^28 + 2^26 + 2^22 + 2^20 + 2^18 + 2^15 + 2^13 - 2^11 + 2^9 + 2^7 + 2^5 - 1"
"r2": 123201
"r2_hex": "0x1e141"
"r2_bit": "2^17 - 2^13 + 2^8 + 2^6 + 1"
"znprimroot": 5
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- "n": 1125896819834881
"n_hex": "0x3ffff48000001"
"n_bit": "2^50 - 2^32 + 2^30 + 2^27 + 1"
"n_fac": "2^27 * 3^2 * 5 * 131 * 1423 + 1"
"nd": 1125896819834879
"nd_hex": "0x3ffff47ffffff"
"nd_bit": "2^50 - 2^32 + 2^30 + 2^27 - 1"
"r2": 26122259521265
"r2_hex": "0x17c20fffdef1"
"r2_bit": "2^45 - 2^43 - 2^38 + 2^33 + 2^28 - 2^13 - 2^8 - 2^4 + 1"
"znprimroot": 14
- "n": 1125892793303041
"n_hex": "0x3fffe58000001"
"n_bit": "2^50 - 2^33 + 2^31 - 2^29 - 2^27 + 1"
"n_fac": "2^27 * 3 * 5 * 7^2 * 101 * 113 + 1"
"nd": 1125892793303039
"nd_hex": "0x3fffe57ffffff"
"nd_bit": "2^50 - 2^33 + 2^31 - 2^29 - 2^27 - 1"
"r2": 319696695939185
"r2_hex": "0x122c32fff5071"
"r2_bit": "2^48 + 2^45 + 2^42 - 2^40 - 2^38 + 2^34 - 2^32 + 2^30 - 2^28 - 2^16 + 2^14 + 2^12 + 2^7 - 2^4 + 1"
"znprimroot": 17
- "n": 1125751864688641
"n_hex": "0x3ffdd88000001"
"n_bit": "2^50 - 2^37 - 2^33 - 2^31 + 2^27 + 1"
"n_fac": "2^27 * 3^2 * 5 * 7 * 26627 + 1"
"nd": 1125751864688639
"nd_hex": "0x3ffdd87ffffff"
"nd_bit": "2^50 - 2^37 - 2^33 - 2^31 + 2^27 - 1"
"r2": 951352819118066
"r2_hex": "0x3614016d6eff2"
"r2_bit": "2^50 - 2^47 - 2^45 + 2^40 + 2^38 + 2^29 - 2^27 - 2^24 - 2^21 - 2^19 - 2^16 - 2^12 - 2^4 + 2"
"znprimroot": 13
- "n": 1125872257990657
"n_hex": "0x3fff990000001"
"n_bit": "2^50 - 2^35 + 2^33 - 2^31 + 2^28 + 1"
"n_fac": "2^28 * 3 * 11 * 149 * 853 + 1"
"nd": 1125872257990655
"nd_hex": "0x3fff98fffffff"
"nd_bit": "2^50 - 2^35 + 2^33 - 2^31 + 2^28 - 1"
"r2": 758895487591345
"r2_hex": "0x2b2361ff5a3b1"
"r2_bit": "2^50 - 2^48 - 2^46 - 2^44 + 2^41 + 2^38 - 2^35 - 2^33 + 2^29 - 2^19 - 2^17 - 2^15 + 2^13 + 2^10 - 2^6 - 2^4 + 1"
"znprimroot": 5
- "n": 1125871452684289
"n_hex": "0x3fff960000001"
"n_bit": "2^50 - 2^35 + 2^33 - 2^31 - 2^29 + 1"
"n_fac": "2^29 * 3^2 * 389 * 599 + 1"
"nd": 1125871452684287
"nd_hex": "0x3fff95fffffff"
"nd_bit": "2^50 - 2^35 + 2^33 - 2^31 - 2^29 - 1"
"r2": 195756018697967
"r2_hex": "0xb209fff506ef"
"r2_bit": "2^48 - 2^46 - 2^44 + 2^41 + 2^35 + 2^33 - 2^20 + 2^18 + 2^16 + 2^11 - 2^8 - 2^4 - 1"
"znprimroot": 7
- "n": 1125845146009601
"n_hex": "0x3fff340000001"
"n_bit": "2^50 - 2^36 + 2^34 - 2^32 + 2^30 + 1"
"n_fac": "2^30 * 5^2 * 41941 + 1"
"nd": 1125845146009599
"nd_hex": "0x3fff33fffffff"
"nd_bit": "2^50 - 2^36 + 2^34 - 2^32 + 2^30 - 1"
"r2": 617183576546176
"r2_hex": "0x231533fd75b80"
"r2_bit": "2^49 + 2^46 - 2^44 + 2^40 + 2^38 + 2^36 + 2^34 - 2^32 + 2^30 - 2^21 - 2^19 - 2^15 - 2^13 - 2^10 - 2^7"
"znprimroot": 3
- "n": 1125844072267777
"n_hex": "0x3fff300000001"
"n_bit": "2^50 - 2^36 + 2^34 - 2^32 + 1"
"n_fac": "2^32 * 3 * 23 * 29 * 131 + 1"
"nd": 1125844072267775
"nd_hex": "0x3fff2ffffffff"
"nd_bit": "2^50 - 2^36 + 2^34 - 2^32 - 1"
"r2": 359381385723768
"r2_hex": "0x146daffd5bf78"
"r2_bit": "2^48 + 2^46 + 2^43 - 2^40 - 2^37 - 2^34 - 2^32 - 2^21 - 2^19 - 2^17 - 2^14 - 2^7 - 2^3"
"znprimroot": 5
- "n": 1125818302464001
"n_hex": "0x3ffed00000001"
"n_bit": "2^50 - 2^36 - 2^34 + 2^32 + 1"
"n_fac": "2^32 * 3^2 * 5^3 * 233 + 1"
"nd": 1125818302463999
"nd_hex": "0x3ffecffffffff"
"nd_bit": "2^50 - 2^36 - 2^34 + 2^32 - 1"
"r2": 808819645333077
"r2_hex": "0x2df9dffa5be55"
"r2_bit": "2^50 - 2^48 - 2^45 - 2^39 + 2^37 - 2^33 - 2^23 + 2^21 + 2^19 - 2^17 - 2^14 - 2^9 + 2^6 + 2^4 + 2^2 + 1"
"znprimroot": 7
- "n": 1125625028935681
"n_hex": "0x3ffc000000001"
"n_bit": "2^50 - 2^38 + 1"
"n_fac": "2^38 * 3^2 * 5 * 7 * 13 + 1"
"nd": 1125625028935679
"nd_hex": "0x3ffbfffffffff"
"nd_bit": "2^50 - 2^38 - 1"
"r2": 549688688637
"r2_hex": "0x7ffbffbffd"
"r2_bit": "2^39 - 2^26 - 2^14 - 2^2 + 1"
"znprimroot": 11
- "n": 1114355034750977
"n_hex": "0x3f58000000001"
"n_bit": "2^50 - 2^43 - 2^41 - 2^39 + 1"
"n_fac": "2^39 * 2027 + 1"
"nd": 1114355034750975
"nd_hex": "0x3f57fffffffff"
"nd_bit": "2^50 - 2^43 - 2^41 - 2^39 - 1"
"r2": 424291881851915
"r2_hex": "0x181e426e61c0b"
"r2_bit": "2^49 - 2^47 + 2^41 - 2^37 + 2^34 + 2^29 + 2^27 - 2^24 - 2^21 + 2^19 - 2^17 + 2^13 - 2^10 + 2^4 - 2^2 - 1"
"znprimroot": 3
- "n": 1096762848706561
"n_hex": "0x3e58000000001"
"n_bit": "2^50 - 2^45 + 2^43 - 2^41 - 2^39 + 1"
"n_fac": "2^39 * 3 * 5 * 7 * 19 + 1"
"nd": 1096762848706559
"nd_hex": "0x3e57fffffffff"
"nd_bit": "2^50 - 2^45 + 2^43 - 2^41 - 2^39 - 1"
"r2": 230673130438222
"r2_hex": "0xd1cbc5ffbe4e"
"r2_bit": "2^48 - 2^46 + 2^44 + 2^41 - 2^38 + 2^36 - 2^34 - 2^30 + 2^27 - 2^25 - 2^14 - 2^9 + 2^6 + 2^4 - 2"
"znprimroot": 61
- "n": 1063777499873281
"n_hex": "0x3c78000000001"
"n_bit": "2^50 - 2^46 + 2^43 - 2^39 + 1"
"n_fac": "2^39 * 3^2 * 5 * 43 + 1"
"nd": 1063777499873279
"nd_hex": "0x3c77fffffffff"
"nd_bit": "2^50 - 2^46 + 2^43 - 2^39 - 1"
"r2": 244312051914892
"r2_hex": "0xde335511988c"
"r2_bit": "2^48 - 2^45 - 2^41 + 2^38 - 2^36 + 2^34 - 2^32 + 2^30 + 2^28 + 2^26 + 2^24 + 2^20 + 2^17 - 2^15 + 2^13 - 2^11 + 2^7 + 2^4 - 2^2"
"znprimroot": 19
- "n": 865865406873601
"n_hex": "0x3138000000001"
"n_bit": "2^50 - 2^48 + 2^44 + 2^42 - 2^39 + 1"
"n_fac": "2^39 * 3^2 * 5^2 * 7 + 1"
"nd": 865865406873599
"nd_hex": "0x3137fffffffff"
"nd_bit": "2^50 - 2^48 + 2^44 + 2^42 - 2^39 - 1"
"r2": 268803017937712
"r2_hex": "0xf47994661330"
"r2_bit": "2^48 - 2^44 + 2^42 + 2^39 - 2^35 + 2^33 - 2^31 + 2^28 + 2^26 + 2^23 - 2^21 + 2^19 - 2^17 + 2^12 + 2^10 - 2^8 + 2^6 - 2^4"
"znprimroot": 31
- "n": 1072023837081601
"n_hex": "0x3cf0000000001"
"n_bit": "2^50 - 2^46 + 2^44 - 2^40 + 1"
"n_fac": "2^40 * 3 * 5^2 * 13 + 1"
"nd": 1072023837081599
"nd_hex": "0x3ceffffffffff"
"nd_bit": "2^50 - 2^46 + 2^44 - 2^40 - 1"
"r2": 962663591322417
"r2_hex": "0x36b8995662331"
"r2_bit": "2^50 - 2^47 - 2^44 - 2^42 - 2^39 + 2^35 + 2^33 - 2^31 + 2^29 - 2^27 - 2^25 - 2^23 - 2^21 + 2^19 - 2^17 + 2^13 + 2^10 - 2^8 + 2^6 - 2^4 + 1"
"znprimroot": 11
- "n": 940082441748481
"n_hex": "0x3570000000001"
"n_bit": "2^50 - 2^47 - 2^45 - 2^43 - 2^40 + 1"
"n_fac": "2^40 * 3^2 * 5 * 19 + 1"
"nd": 940082441748479
"nd_hex": "0x356ffffffffff"
"nd_bit": "2^50 - 2^47 - 2^45 - 2^43 - 2^40 - 1"
"r2": 38037958407003
"r2_hex": "0x229866ffb35b"
"r2_bit": "2^45 + 2^41 + 2^39 + 2^37 - 2^35 + 2^31 - 2^29 + 2^27 - 2^24 - 2^14 - 2^12 + 2^10 - 2^7 - 2^5 - 2^2 - 1"
"znprimroot": 7
- "n": 1022545813831681
"n_hex": "0x3a20000000001"
"n_bit": "2^50 - 2^47 + 2^45 + 2^41 + 1"
"n_fac": "2^41 * 3 * 5 * 31 + 1"
"nd": 1022545813831679
"nd_hex": "0x3a1ffffffffff"
"nd_bit": "2^50 - 2^47 + 2^45 + 2^41 - 1"
"r2": 295217689787290
"r2_hex": "0x10c7fb987fb9a"
"r2_bit": "2^48 + 2^44 - 2^42 + 2^39 - 2^30 - 2^27 + 2^25 - 2^23 + 2^19 - 2^10 - 2^7 + 2^5 - 2^3 + 2"
"znprimroot": 11
- "n": 659706976665601
"n_hex": "0x2580000000001"
"n_bit": "2^49 + 2^47 - 2^45 - 2^43 + 1"
"n_fac": "2^43 * 3 * 5^2 + 1"
"nd": 659706976665599
"nd_hex": "0x257ffffffffff"
"nd_bit": "2^49 + 2^47 - 2^45 - 2^43 - 1"
"r2": 471001461029168
"r2_hex": "0x1ac5f92c5f930"
"r2_bit": "2^49 - 2^46 - 2^44 - 2^42 + 2^39 - 2^37 - 2^31 + 2^28 + 2^26 - 2^24 - 2^22 + 2^19 - 2^17 - 2^11 + 2^8 + 2^6 - 2^4"
"znprimroot": 11
- "n": 1108307720798209
"n_hex": "0x3f00000000001"
"n_bit": "2^50 - 2^44 + 1"
"n_fac": "2^44 * 3^2 * 7 + 1"
"nd": 1108307720798207
"nd_hex": "0x3efffffffffff"
"nd_bit": "2^50 - 2^44 - 1"
"r2": 34905131040509
"r2_hex": "0x1fbefbefbefd"
"r2_bit": "2^45 - 2^38 - 2^32 - 2^26 - 2^20 - 2^14 - 2^8 - 2^2 + 1"
"znprimroot": 11
- "n": 263882790666241
"n_hex": "0xf00000000001"
"n_bit": "2^48 - 2^44 + 1"
"n_fac": "2^44 * 3 * 5 + 1"
"nd": 263882790666239
"nd_hex": "0xefffffffffff"
"nd_bit": "2^48 - 2^44 - 1"
"r2": 227525606174466
"r2_hex": "0xceeeeeeeef02"
"r2_bit": "2^48 - 2^46 + 2^44 - 2^40 - 2^36 - 2^32 - 2^28 - 2^24 - 2^20 - 2^16 - 2^12 - 2^8 + 2"
"znprimroot": 7
Raw
result_prime_0051.yaml
- "r": 51
"primes":
- "n": 2251799813685119
"n_hex": "0x7ffffffffff7f"
"n_bit": "2^51 - 2^7 - 1"
"n_fac": "2 * 701 * 1531 * 1049075089 + 1"
"nd": 1693213813391233
"nd_hex": "0x603f80fe03f81"
"nd_bit": "2^51 - 2^49 + 2^42 - 2^35 + 2^28 - 2^21 + 2^14 - 2^7 + 1"
"r2": 16641
"r2_hex": "0x4101"
"r2_bit": "2^14 + 2^8 + 1"
"znprimroot": 11
- "n": 2251799813683351
"n_hex": "0x7fffffffff897"
"n_bit": "2^51 - 2^11 + 2^7 + 2^5 - 2^3 - 1"
"n_fac": "2 * 3^2 * 5^2 * 7 * 714857083709c + 1"
"nd": 1835151561390297
"nd_hex": "0x6850f84ecf8d9"
"nd_bit": "2^51 - 2^49 + 2^47 + 2^42 + 2^40 + 2^36 - 2^31 + 2^26 + 2^24 - 2^20 - 2^18 + 2^16 - 2^11 + 2^8 - 2^5 - 2^3 + 1"
"r2": 3598609
"r2_hex": "0x36e911"
"r2_bit": "2^22 - 2^19 - 2^16 - 2^13 + 2^11 + 2^8 + 2^4 + 1"
"znprimroot": 6
- "n": 2251799813685109
"n_hex": "0x7ffffffffff75"
"n_bit": "2^51 - 2^7 - 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3 * 433 * 433371788623 + 1"
"nd": 2089799827089187
"nd_hex": "0x76ca970586723"
"nd_bit": "2^51 - 2^47 - 2^44 - 2^42 + 2^39 + 2^37 + 2^35 + 2^33 - 2^31 - 2^28 + 2^23 - 2^21 - 2^19 + 2^15 - 2^13 + 2^11 - 2^8 + 2^5 + 2^2 - 1"
"r2": 19321
"r2_hex": "0x4b79"
"r2_bit": "2^14 + 2^12 - 2^10 - 2^7 - 2^3 + 1"
"znprimroot": 6
- "n": 2251799813683261
"n_hex": "0x7fffffffff83d"
"n_bit": "2^51 - 2^11 + 2^6 - 2^2 + 1"
"n_fac": "2^2 * 3^3 * 5 * 19 * 53 * 2617 * 1582351 + 1"
"nd": 2107875014320363
"nd_hex": "0x77d19e575a0eb"
"nd_bit": "2^51 - 2^47 - 2^42 + 2^40 + 2^37 - 2^35 + 2^33 - 2^29 + 2^27 - 2^25 - 2^23 - 2^19 - 2^17 - 2^15 + 2^13 + 2^8 - 2^4 - 2^2 - 1"
"r2": 3948169
"r2_hex": "0x3c3e89"
"r2_bit": "2^22 - 2^18 + 2^14 - 2^9 + 2^7 + 2^3 + 1"
"znprimroot": 10
- "n": 2251799813685017
"n_hex": "0x7ffffffffff19"
"n_bit": "2^51 - 2^8 + 2^5 - 2^3 + 1"
"n_fac": "2^3 * 7 * 181 * 222158624081c + 1"
"nd": 1764397256610519
"nd_hex": "0x644b5bfb912d7"
"nd_bit": "2^51 - 2^49 + 2^46 + 2^42 + 2^40 - 2^38 - 2^35 - 2^33 - 2^30 - 2^22 - 2^19 + 2^16 + 2^12 + 2^10 - 2^8 - 2^5 - 2^3 - 1"
"r2": 53361
"r2_hex": "0xd071"
"r2_bit": "2^16 - 2^14 + 2^12 + 2^7 - 2^4 + 1"
"znprimroot": 3
- "n": 2251799813685001
"n_hex": "0x7ffffffffff09"
"n_bit": "2^51 - 2^8 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5^4 * 150119987579c + 1"
"nd": 1139574804496583
"nd_hex": "0x40c6fef6ac0c7"
"nd_bit": "2^50 + 2^44 - 2^42 + 2^39 - 2^36 - 2^28 - 2^23 - 2^20 - 2^18 - 2^16 - 2^14 + 2^8 - 2^6 + 2^3 - 1"
"r2": 61009
"r2_hex": "0xee51"
"r2_bit": "2^16 - 2^12 - 2^9 + 2^6 + 2^4 + 1"
"znprimroot": 14
- "n": 2251799813684809
"n_hex": "0x7fffffffffe49"
"n_bit": "2^51 - 2^9 + 2^6 + 2^3 + 1"
"n_fac": "2^3 * 3^2 * 31274997412289c + 1"
"nd": 1749120128625671
"nd_hex": "0x636d0c3efac07"
"nd_bit": "2^51 - 2^49 + 2^46 - 2^43 - 2^40 - 2^38 + 2^36 + 2^32 - 2^30 + 2^26 - 2^20 - 2^14 - 2^12 - 2^10 + 2^3 - 1"
"r2": 192721
"r2_hex": "0x2f0d1"
"r2_bit": "2^18 - 2^16 - 2^12 + 2^8 - 2^6 + 2^4 + 1"
"znprimroot": 7
- "n": 2251799813684753
"n_hex": "0x7fffffffffe11"
"n_bit": "2^51 - 2^9 + 2^4 + 1"
"n_fac": "2^4 * 23 * 67 * 91328675117 + 1"
"nd": 2174465274629391
"nd_hex": "0x7b9aa26454d0f"
"nd_bit": "2^51 - 2^46 - 2^43 + 2^41 - 2^39 + 2^37 + 2^35 + 2^33 + 2^29 + 2^27 - 2^25 + 2^22 + 2^18 + 2^16 + 2^14 + 2^12 - 2^10 + 2^8 + 2^4 - 1"
"r2": 245025
"r2_hex": "0x3bd21"
"r2_bit": "2^18 - 2^14 - 2^10 + 2^8 + 2^5 + 1"
"znprimroot": 3
- "n": 2251799813684401
"n_hex": "0x7fffffffffcb1"
"n_bit": "2^51 - 2^10 + 2^8 - 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5^2 * 7 * 19 * 139 * 101503751 + 1"
"nd": 685908325774255
"nd_hex": "0x26fd47a1b33af"
"nd_bit": "2^49 + 2^47 - 2^44 - 2^38 + 2^36 + 2^34 + 2^31 - 2^27 + 2^25 + 2^21 - 2^18 - 2^16 + 2^14 - 2^12 + 2^10 - 2^6 - 2^4 - 1"
"r2": 717409
"r2_hex": "0xaf261"
"r2_bit": "2^20 - 2^18 - 2^16 - 2^12 + 2^9 + 2^7 - 2^5 + 1"
"znprimroot": 11
- "n": 2251799813682721
"n_hex": "0x7fffffffff621"
"n_bit": "2^51 - 2^11 - 2^9 + 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5 * 7 * 1021 * 72932693 + 1"
"nd": 1533576366977567
"nd_hex": "0x572c79296f21f"
"nd_bit": "2^51 - 2^49 - 2^47 - 2^44 + 2^42 - 2^40 - 2^38 + 2^35 - 2^31 + 2^28 + 2^25 + 2^23 + 2^21 - 2^19 - 2^16 - 2^12 + 2^9 + 2^5 - 1"
"r2": 6385729
"r2_hex": "0x617041"
"r2_bit": "2^23 - 2^21 + 2^17 - 2^15 - 2^12 + 2^6 + 1"
"znprimroot": 19
- "n": 2251799813511361
"n_hex": "0x7fffffffd58c1"
"n_bit": "2^51 - 2^17 - 2^15 - 2^13 - 2^11 + 2^8 - 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 7 * 43 * 953 * 2725699 + 1"
"nd": 2147631717730495
"nd_hex": "0x7a14279a4c8bf"
"nd_bit": "2^51 - 2^47 + 2^45 + 2^40 + 2^38 + 2^33 + 2^31 - 2^27 + 2^25 - 2^23 + 2^21 + 2^18 + 2^16 - 2^14 + 2^11 + 2^8 - 2^6 - 1"
"r2": 30236688769
"r2_hex": "0x70a3f4181"
"r2_bit": "2^35 - 2^32 + 2^27 + 2^25 + 2^22 - 2^16 + 2^14 + 2^9 - 2^7 + 1"
"znprimroot": 17
- "n": 2251799813681281
"n_hex": "0x7fffffffff081"
"n_bit": "2^51 - 2^12 + 2^7 + 1"
"n_fac": "2^7 * 3^2 * 5 * 390937467653 + 1"
"nd": 1501389086765183
"nd_hex": "0x55581632fb07f"
"nd_bit": "2^51 - 2^49 - 2^47 - 2^45 - 2^43 - 2^41 - 2^39 + 2^33 - 2^31 - 2^29 + 2^26 - 2^24 + 2^22 - 2^20 - 2^14 - 2^12 + 2^7 - 1"
"r2": 15737089
"r2_hex": "0xf02101"
"r2_bit": "2^24 - 2^20 + 2^13 + 2^8 + 1"
"znprimroot": 11
- "n": 2251799813316481
"n_hex": "0x7fffffffa5f81"
"n_bit": "2^51 - 2^19 + 2^17 + 2^15 - 2^13 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 7 * 167544628967c + 1"
"nd": 729036577447807
"nd_hex": "0x2970e0e3a1f7f"
"nd_bit": "2^49 + 2^47 + 2^45 - 2^43 - 2^40 + 2^36 - 2^33 + 2^28 - 2^25 + 2^22 - 2^19 + 2^17 + 2^13 - 2^7 - 1"
"r2": 135989100289
"r2_hex": "0x1fa994ff01"
"r2_bit": "2^37 - 2^31 + 2^29 + 2^27 + 2^25 - 2^23 + 2^20 + 2^18 + 2^16 - 2^8 + 1"
"znprimroot": 33
- "n": 2251799813640961
"n_hex": "0x7ffffffff5301"
"n_bit": "2^51 - 2^16 + 2^14 + 2^12 + 2^10 - 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5 * 11 * 23 * 137 * 277 * 20359 + 1"
"nd": 905916347470591
"nd_hex": "0x337ed161652ff"
"nd_bit": "2^50 - 2^48 + 2^46 - 2^43 - 2^36 - 2^34 + 2^32 + 2^29 - 2^27 - 2^25 + 2^21 - 2^19 - 2^17 + 2^14 + 2^12 + 2^10 - 2^8 - 1"
"r2": 1961338369
"r2_hex": "0x74e7a601"
"r2_bit": "2^31 - 2^28 + 2^26 + 2^24 - 2^21 + 2^19 - 2^15 + 2^13 + 2^11 - 2^9 + 1"
"znprimroot": 17
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"nd": 2049214796267519
"nd_hex": "0x747bfffffffff"
"nd_bit": "2^51 - 2^48 + 2^46 + 2^43 - 2^38 - 1"
"r2": 1743864009364430
"r2_hex": "0x63208fad093ce"
"r2_bit": "2^51 - 2^49 + 2^46 - 2^44 + 2^41 + 2^35 + 2^32 - 2^26 - 2^24 - 2^22 + 2^20 + 2^15 + 2^12 + 2^10 - 2^6 + 2^4 - 2"
"znprimroot": 38
- "n": 1298798110310401
"n_hex": "0x49d4000000001"
"n_bit": "2^50 + 2^47 + 2^45 - 2^42 + 2^40 + 2^38 + 1"
"n_fac": "2^38 * 3^3 * 5^2 * 7 + 1"
"nd": 1298798110310399
"nd_hex": "0x49d3fffffffff"
"nd_bit": "2^50 + 2^47 + 2^45 - 2^42 + 2^40 + 2^38 - 1"
"r2": 429652261046398
"r2_hex": "0x186c43665887e"
"r2_bit": "2^49 - 2^47 + 2^43 - 2^40 - 2^38 + 2^34 + 2^30 - 2^27 - 2^25 + 2^23 - 2^21 + 2^19 - 2^17 - 2^15 + 2^11 + 2^7 - 2"
"znprimroot": 17
- "n": 2249051034615809
"n_hex": "0x7fd8000000001"
"n_bit": "2^51 - 2^41 - 2^39 + 1"
"n_fac": "2^39 * 4091 + 1"
"nd": 2249051034615807
"nd_hex": "0x7fd7fffffffff"
"nd_bit": "2^51 - 2^41 - 2^39 - 1"
"r2": 244088221822067
"r2_hex": "0xddff37c16c73"
"r2_bit": "2^48 - 2^45 - 2^41 - 2^32 + 2^30 - 2^27 - 2^22 + 2^17 - 2^15 - 2^12 - 2^10 + 2^7 - 2^4 + 2^2 - 1"
"znprimroot": 3
- "n": 1096762848706561
"n_hex": "0x3e58000000001"
"n_bit": "2^50 - 2^45 + 2^43 - 2^41 - 2^39 + 1"
"n_fac": "2^39 * 3 * 5 * 7 * 19 + 1"
"nd": 1096762848706559
"nd_hex": "0x3e57fffffffff"
"nd_bit": "2^50 - 2^45 + 2^43 - 2^41 - 2^39 - 1"
"r2": 922692521752888
"r2_hex": "0x3472f17fef938"
"r2_bit": "2^50 - 2^48 + 2^46 + 2^43 - 2^40 + 2^38 - 2^36 - 2^32 + 2^29 - 2^27 - 2^16 - 2^11 + 2^8 + 2^6 - 2^3"
"znprimroot": 61
- "n": 865865406873601
"n_hex": "0x3138000000001"
"n_bit": "2^50 - 2^48 + 2^44 + 2^42 - 2^39 + 1"
"n_fac": "2^39 * 3^2 * 5^2 * 7 + 1"
"nd": 865865406873599
"nd_hex": "0x3137fffffffff"
"nd_bit": "2^50 - 2^48 + 2^44 + 2^42 - 2^39 - 1"
"r2": 209346664877247
"r2_hex": "0xbe6651984cbf"
"r2_bit": "2^48 - 2^46 - 2^41 + 2^39 - 2^37 + 2^35 - 2^33 + 2^30 + 2^28 + 2^25 - 2^23 + 2^21 - 2^19 + 2^14 + 2^12 - 2^10 + 2^8 - 2^6 - 1"
"znprimroot": 31
- "n": 2244103232290817
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"n_bit": "2^51 - 2^43 + 2^40 + 1"
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"nd": 2244103232290815
"nd_hex": "0x7f8ffffffffff"
"nd_bit": "2^51 - 2^43 + 2^40 - 1"
"r2": 74740393790307
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"r2_bit": "2^46 + 2^42 - 2^35 + 2^33 - 2^29 - 2^27 + 2^25 + 2^23 + 2^21 - 2^16 + 2^14 + 2^12 - 2^10 - 2^7 - 2^5 + 2^2 - 1"
"znprimroot": 3
- "n": 2226511046246401
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"nd": 2226511046246399
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"nd_bit": "2^51 - 2^45 + 2^43 + 2^40 - 1"
"r2": 943093746186825
"r2_hex": "0x359bd1fbb3a49"
"r2_bit": "2^50 - 2^47 - 2^45 - 2^43 + 2^41 - 2^38 - 2^34 + 2^32 + 2^29 - 2^22 - 2^18 - 2^16 + 2^14 - 2^11 + 2^9 + 2^6 + 2^3 + 1"
"znprimroot": 7
- "n": 1880164883496961
"n_hex": "0x6ae0000000001"
"n_bit": "2^51 - 2^48 - 2^46 - 2^44 - 2^41 + 1"
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"nd": 1880164883496959
"nd_hex": "0x6adffffffffff"
"nd_bit": "2^51 - 2^48 - 2^46 - 2^44 - 2^41 - 1"
"r2": 968879358568117
"r2_hex": "0x37130cdff66b5"
"r2_bit": "2^50 - 2^47 - 2^44 + 2^40 + 2^38 - 2^36 + 2^32 - 2^30 + 2^28 - 2^25 - 2^15 - 2^13 + 2^11 - 2^8 - 2^6 - 2^4 + 2^2 + 1"
"znprimroot": 7
- "n": 2221013488107521
"n_hex": "0x7e40000000001"
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"n_fac": "2^42 * 5 * 101 + 1"
"nd": 2221013488107519
"nd_hex": "0x7e3ffffffffff"
"nd_bit": "2^51 - 2^45 + 2^42 - 1"
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"r2_bit": "2^51 - 2^47 - 2^44 + 2^42 - 2^39 + 2^37 - 2^34 + 2^31 + 2^29 + 2^26 + 2^22 - 2^16 - 2^13 - 2^10 + 2^2"
"znprimroot": 6
- "n": 2097868185796609
"n_hex": "0x7740000000001"
"n_bit": "2^51 - 2^47 - 2^44 + 2^42 + 1"
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"nd": 2097868185796607
"nd_hex": "0x773ffffffffff"
"nd_bit": "2^51 - 2^47 - 2^44 + 2^42 - 1"
"r2": 1506031272796076
"r2_hex": "0x559ba3b091fac"
"r2_bit": "2^51 - 2^49 - 2^47 - 2^45 - 2^43 + 2^41 - 2^38 - 2^35 + 2^33 + 2^30 - 2^26 - 2^24 + 2^19 + 2^16 + 2^13 - 2^6 - 2^4 - 2^2"
"znprimroot": 19
- "n": 2190227162529793
"n_hex": "0x7c80000000001"
"n_bit": "2^51 - 2^46 + 2^43 + 1"
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"nd": 2190227162529791
"nd_hex": "0x7c7ffffffffff"
"nd_bit": "2^51 - 2^46 + 2^43 - 1"
"r2": 341316669801502
"r2_hex": "0x1366cfadc041e"
"r2_bit": "2^48 + 2^46 - 2^43 - 2^41 + 2^39 - 2^36 - 2^34 + 2^32 - 2^26 - 2^24 - 2^21 - 2^18 + 2^10 + 2^5 - 2"
"znprimroot": 10
- "n": 1451355348664321
"n_hex": "0x5280000000001"
"n_bit": "2^50 + 2^48 + 2^45 + 2^43 + 1"
"n_fac": "2^43 * 3 * 5 * 11 + 1"
"nd": 1451355348664319
"nd_hex": "0x527ffffffffff"
"nd_bit": "2^50 + 2^48 + 2^45 + 2^43 - 1"
"r2": 139084889060249
"r2_hex": "0x7e7f3967f399"
"r2_bit": "2^47 - 2^41 + 2^39 - 2^32 + 2^30 - 2^27 + 2^25 - 2^23 - 2^21 + 2^19 - 2^12 + 2^10 - 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 17
- "n": 2128654511374337
"n_hex": "0x7900000000001"
"n_bit": "2^51 - 2^47 + 2^44 + 1"
"n_fac": "2^44 * 11^2 + 1"
"nd": 2128654511374335
"nd_hex": "0x78fffffffffff"
"nd_bit": "2^51 - 2^47 + 2^44 - 1"
"r2": 1734502309999034
"r2_hex": "0x629854a0cb1ba"
"r2_bit": "2^51 - 2^49 + 2^45 + 2^43 + 2^41 - 2^39 + 2^34 + 2^32 + 2^30 + 2^27 + 2^25 + 2^20 - 2^18 + 2^16 - 2^14 - 2^12 + 2^9 - 2^6 - 2^3 + 2"
"znprimroot": 3
- "n": 1952732650930177
"n_hex": "0x6f00000000001"
"n_bit": "2^51 - 2^48 - 2^44 + 1"
"n_fac": "2^44 * 3 * 37 + 1"
"nd": 1952732650930175
"nd_hex": "0x6efffffffffff"
"nd_bit": "2^51 - 2^48 - 2^44 - 1"
"r2": 376409386085479
"r2_hex": "0x15657a3bf6c67"
"r2_bit": "2^49 - 2^47 - 2^45 - 2^43 - 2^41 + 2^39 - 2^37 - 2^35 - 2^31 + 2^29 + 2^26 - 2^22 - 2^15 - 2^12 - 2^10 + 2^7 - 2^5 + 2^3 - 1"
"znprimroot": 5
- "n": 263882790666241
"n_hex": "0xf00000000001"
"n_bit": "2^48 - 2^44 + 1"
"n_fac": "2^44 * 3 * 5 + 1"
"nd": 263882790666239
"nd_hex": "0xefffffffffff"
"nd_bit": "2^48 - 2^44 - 1"
"r2": 118454052699141
"r2_hex": "0x6bbbbbbbbc05"
"r2_bit": "2^47 - 2^44 - 2^42 - 2^38 - 2^34 - 2^30 - 2^26 - 2^22 - 2^18 - 2^14 - 2^10 + 2^2 + 1"
"znprimroot": 7
- "n": 1899956092796929
"n_hex": "0x6c00000000001"
"n_bit": "2^51 - 2^48 - 2^46 + 1"
"n_fac": "2^46 * 3^3 + 1"
"nd": 1899956092796927
"nd_hex": "0x6bfffffffffff"
"nd_bit": "2^51 - 2^48 - 2^46 - 1"
"r2": 1412587383121998
"r2_hex": "0x504bda12f684e"
"r2_bit": "2^50 + 2^48 + 2^42 + 2^40 - 2^38 - 2^33 - 2^31 + 2^29 + 2^24 + 2^22 - 2^20 - 2^15 - 2^13 + 2^11 + 2^6 + 2^4 - 2"
"znprimroot": 7
Raw
result_prime_0052.yaml
- "r": 52
"primes":
- "n": 4503599627370211
"n_hex": "0xffffffffffee3"
"n_bit": "2^52 - 2^8 - 2^5 + 2^2 - 1"
"n_fac": "2 * 3^2 * 5 * 409 * 122347178141 + 1"
"nd": 3539671286073653
"nd_hex": "0xc934ff1a0c935"
"nd_bit": "2^52 - 2^50 + 2^47 + 2^44 + 2^42 - 2^40 + 2^38 + 2^36 - 2^28 + 2^25 - 2^23 + 2^21 + 2^16 - 2^14 + 2^11 + 2^8 + 2^6 - 2^4 + 2^2 + 1"
"r2": 81225
"r2_hex": "0x13d49"
"r2_bit": "2^16 + 2^14 - 2^10 + 2^8 + 2^6 + 2^3 + 1"
"znprimroot": 3
- "n": 4503599627369797
"n_hex": "0xffffffffffd45"
"n_bit": "2^52 - 2^10 + 2^8 + 2^6 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 1297 * 96453345913 + 1"
"nd": 4091252880372339
"nd_hex": "0xe88f90a9ef273"
"nd_bit": "2^52 - 2^49 + 2^47 + 2^43 + 2^40 - 2^35 + 2^32 + 2^27 + 2^25 + 2^23 + 2^21 - 2^16 - 2^12 + 2^9 + 2^7 - 2^4 + 2^2 - 1"
"r2": 488601
"r2_hex": "0x77499"
"r2_bit": "2^19 - 2^15 - 2^12 + 2^10 + 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 5
- "n": 4503599627368381
"n_hex": "0xffffffffff7bd"
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"n_fac": "2^2 * 3 * 5 * 7 * 11 * 974805114149c + 1"
"nd": 2425342778049643
"nd_hex": "0x89dd61ebe846b"
"nd_bit": "2^51 + 2^47 + 2^45 - 2^41 - 2^37 - 2^35 - 2^33 + 2^29 - 2^24 - 2^22 - 2^17 + 2^15 + 2^10 + 2^7 - 2^4 - 2^2 - 1"
"r2": 4473225
"r2_hex": "0x444189"
"r2_bit": "2^22 + 2^18 + 2^14 + 2^9 - 2^7 + 2^3 + 1"
"znprimroot": 18
- "n": 4503599627366701
"n_hex": "0xffffffffff12d"
"n_bit": "2^52 - 2^12 + 2^8 + 2^6 - 2^4 - 2^2 + 1"
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"nd": 2829138738248027
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"nd_bit": "2^51 + 2^49 + 2^44 - 2^42 + 2^40 + 2^37 - 2^35 - 2^33 + 2^30 - 2^28 + 2^25 - 2^23 + 2^18 - 2^15 - 2^11 + 2^9 - 2^7 - 2^5 - 2^2 - 1"
"r2": 14402025
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"znprimroot": 6
- "n": 4503599627370313
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"nd": 2707081743228167
"nd_hex": "0x99e1395aedd07"
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"r2": 33489
"r2_hex": "0x82d1"
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"znprimroot": 10
- "n": 4503599627366089
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"n_fac": "2^3 * 3^3 * 71 * 293661947533c + 1"
"nd": 2408664470549639
"nd_hex": "0x88eaae6267487"
"nd_bit": "2^51 + 2^47 + 2^44 - 2^40 - 2^38 - 2^36 - 2^34 - 2^32 - 2^29 + 2^27 - 2^25 + 2^21 + 2^19 - 2^17 + 2^15 - 2^12 + 2^10 + 2^7 + 2^3 - 1"
"r2": 19421649
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"r2_bit": "2^24 + 2^21 + 2^19 + 2^15 - 2^13 - 2^11 + 2^9 - 2^6 + 2^4 + 1"
"znprimroot": 14
- "n": 4503599627361481
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"n_fac": "2^3 * 3^2 * 5 * 41 * 293 * 1041371761 + 1"
"nd": 4278294754165383
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"nd_bit": "2^52 - 2^48 + 2^46 - 2^44 + 2^42 - 2^40 + 2^37 - 2^35 - 2^33 + 2^29 - 2^24 + 2^20 + 2^16 + 2^9 + 2^7 + 2^3 - 1"
"r2": 81270225
"r2_hex": "0x4d815d1"
"r2_bit": "2^26 + 2^24 - 2^21 - 2^19 + 2^13 - 2^11 - 2^9 - 2^6 + 2^4 + 1"
"znprimroot": 7
- "n": 4503599627370449
"n_hex": "0xfffffffffffd1"
"n_bit": "2^52 - 2^6 + 2^4 + 1"
"n_fac": "2^4 * 11 * 167 * 239 * 641110271 + 1"
"nd": 1054033955342031
"nd_hex": "0x3bea3677d46cf"
"nd_bit": "2^50 - 2^46 - 2^41 + 2^39 + 2^37 + 2^34 - 2^31 - 2^29 + 2^27 - 2^23 - 2^18 + 2^16 + 2^14 + 2^11 - 2^8 - 2^6 + 2^4 - 1"
"r2": 2209
"r2_hex": "0x8a1"
"r2_bit": "2^11 + 2^7 + 2^5 + 1"
"znprimroot": 3
- "n": 4503599627370001
"n_hex": "0xffffffffffe11"
"n_bit": "2^52 - 2^9 + 2^4 + 1"
"n_fac": "2^4 * 3 * 5^4 * 150119987579c + 1"
"nd": 2174465274629391
"nd_hex": "0x7b9aa26454d0f"
"nd_bit": "2^51 - 2^46 - 2^43 + 2^41 - 2^39 + 2^37 + 2^35 + 2^33 + 2^29 + 2^27 - 2^25 + 2^22 + 2^18 + 2^16 + 2^14 + 2^12 - 2^10 + 2^8 + 2^4 - 1"
"r2": 245025
"r2_hex": "0x3bd21"
"r2_bit": "2^18 - 2^14 - 2^10 + 2^8 + 2^5 + 1"
"znprimroot": 23
- "n": 4503599627365009
"n_hex": "0xfffffffffea91"
"n_bit": "2^52 - 2^13 + 2^11 + 2^9 + 2^7 + 2^4 + 1"
"n_fac": "2^4 * 3^5 * 809 * 9349 * 153151 + 1"
"nd": 1545521796671887
"nd_hex": "0x57da4d5aee98f"
"nd_bit": "2^51 - 2^49 - 2^47 - 2^41 - 2^39 + 2^37 + 2^34 + 2^32 - 2^29 - 2^27 - 2^25 - 2^22 - 2^20 - 2^16 - 2^13 + 2^11 + 2^9 - 2^7 + 2^4 - 1"
"r2": 30107169
"r2_hex": "0x1cb6621"
"r2_bit": "2^25 - 2^22 + 2^20 - 2^18 - 2^15 - 2^13 + 2^11 - 2^9 + 2^5 + 1"
"znprimroot": 11
- "n": 4503599627363761
"n_hex": "0xfffffffffe5b1"
"n_bit": "2^52 - 2^13 + 2^11 - 2^9 - 2^6 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5 * 7 * 11 * 617 * 394977761 + 1"
"nd": 1985328477158575
"nd_hex": "0x70da54ea4bcaf"
"nd_bit": "2^51 - 2^48 + 2^44 - 2^41 - 2^39 + 2^37 + 2^34 + 2^32 + 2^30 + 2^28 - 2^25 + 2^23 + 2^21 + 2^18 + 2^16 - 2^14 - 2^10 + 2^8 - 2^6 - 2^4 - 1"
"r2": 45360225
"r2_hex": "0x2b42461"
"r2_bit": "2^26 - 2^24 - 2^22 - 2^20 + 2^18 + 2^13 + 2^10 + 2^7 - 2^5 + 1"
"znprimroot": 13
- "n": 4503599627351761
"n_hex": "0xfffffffffb6d1"
"n_bit": "2^52 - 2^14 - 2^11 - 2^8 - 2^6 + 2^4 + 1"
"n_fac": "2^4 * 3^2 * 5 * 13^2 * 359 * 103097023 + 1"
"nd": 3024995874610639
"nd_hex": "0xabf37bc8d9dcf"
"nd_bit": "2^52 - 2^50 - 2^48 - 2^46 - 2^40 + 2^38 - 2^35 - 2^30 - 2^26 + 2^23 + 2^20 - 2^17 - 2^15 + 2^13 - 2^9 - 2^6 + 2^4 - 1"
"r2": 351000225
"r2_hex": "0x14ebd6a1"
"r2_bit": "2^28 + 2^26 + 2^24 - 2^20 - 2^18 - 2^13 - 2^11 - 2^9 + 2^7 + 2^5 + 1"
"znprimroot": 7
- "n": 4503599627340241
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"n_fac": "2^4 * 3^2 * 5 * 7 * 893571354631 + 1"
"nd": 2900285411987663
"nd_hex": "0xa4dcb51ba90cf"
"nd_bit": "2^51 + 2^49 + 2^46 + 2^44 - 2^41 - 2^38 + 2^36 - 2^34 - 2^32 + 2^30 + 2^28 + 2^25 - 2^22 - 2^19 + 2^17 + 2^15 + 2^12 + 2^8 - 2^6 + 2^4 - 1"
"r2": 915365025
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"znprimroot": 11
- "n": 4503599627368993
"n_hex": "0xffffffffffa21"
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"n_fac": "2^5 * 3 * 359 * 130675476653 + 1"
"nd": 1740912430806559
"nd_hex": "0x62f59c305f61f"
"nd_bit": "2^51 - 2^49 + 2^46 - 2^44 - 2^39 - 2^37 - 2^35 + 2^33 - 2^30 + 2^26 - 2^24 + 2^19 - 2^17 - 2^11 - 2^9 + 2^5 - 1"
"r2": 2259009
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"znprimroot": 13
- "n": 4503599627364577
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"n_bit": "2^52 - 2^13 + 2^11 + 2^8 - 2^5 + 1"
"n_fac": "2^5 * 3^3 * 83 * 62801199623 + 1"
"nd": 3423161804956895
"nd_hex": "0xc2958f764a4df"
"nd_bit": "2^52 - 2^50 + 2^45 + 2^43 + 2^41 - 2^39 - 2^37 - 2^35 + 2^32 - 2^27 - 2^23 - 2^21 + 2^18 + 2^15 + 2^13 + 2^10 + 2^8 - 2^5 - 1"
"r2": 35034561
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"r2_bit": "2^25 + 2^21 - 2^19 - 2^17 + 2^15 + 2^13 - 2^11 - 2^9 - 2^6 + 1"
"znprimroot": 5
- "n": 4503599627321761
"n_hex": "0xfffffffff41a1"
"n_bit": "2^52 - 2^16 + 2^14 + 2^9 - 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 7 * 31 * 43237323611c + 1"
"nd": 3365478502702495
"nd_hex": "0xbf4e286a71d9f"
"nd_bit": "2^52 - 2^50 - 2^44 + 2^42 + 2^40 - 2^37 + 2^33 + 2^31 + 2^27 - 2^25 + 2^23 + 2^21 + 2^19 - 2^16 + 2^13 - 2^9 - 2^7 + 2^5 - 1"
"r2": 2375100225
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"r2_bit": "2^31 + 2^28 - 2^25 - 2^23 + 2^20 + 2^16 + 2^13 + 2^11 - 2^8 + 2^6 + 1"
"znprimroot": 22
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"nd_bit": "2^52 - 2^37 - 2^34 - 1"
"r2": 1153731289612107
"r2_hex": "0x4194fffaeff4b"
"r2_bit": "2^50 + 2^45 - 2^43 + 2^40 + 2^38 + 2^36 - 2^22 - 2^20 - 2^16 - 2^8 + 2^6 + 2^4 - 2^2 - 1"
"znprimroot": 3
- "n": 4502963972210689
"n_hex": "0xfff6c00000001"
"n_bit": "2^52 - 2^39 - 2^36 - 2^34 + 1"
"n_fac": "2^34 * 3^2 * 29123 + 1"
"nd": 4502963972210687
"nd_hex": "0xfff6bffffffff"
"nd_bit": "2^52 - 2^39 - 2^36 - 2^34 - 1"
"r2": 168001851018888
"r2_hex": "0x98cbfaa6ce88"
"r2_bit": "2^47 + 2^45 - 2^43 + 2^40 - 2^38 + 2^36 - 2^34 - 2^27 + 2^25 + 2^23 + 2^21 + 2^19 - 2^16 - 2^14 + 2^12 - 2^9 + 2^7 + 2^3"
"znprimroot": 13
- "n": 4501211625553921
"n_hex": "0xffdd400000001"
"n_bit": "2^52 - 2^41 - 2^38 + 2^36 + 2^34 + 1"
"n_fac": "2^34 * 3 * 5 * 17467 + 1"
"nd": 4501211625553919
"nd_hex": "0xffdd3ffffffff"
"nd_bit": "2^52 - 2^41 - 2^38 + 2^36 + 2^34 - 1"
"r2": 4255555409199089
"r2_hex": "0xf1e67b47cbff1"
"r2_bit": "2^52 - 2^48 + 2^45 - 2^41 + 2^39 - 2^37 + 2^35 - 2^30 - 2^28 + 2^26 + 2^23 - 2^18 + 2^16 - 2^14 - 2^4 + 1"
"znprimroot": 13
- "n": 4500696229478401
"n_hex": "0xffd5c00000001"
"n_bit": "2^52 - 2^41 - 2^39 - 2^37 - 2^34 + 1"
"n_fac": "2^34 * 3 * 5^2 * 7 * 499 + 1"
"nd": 4500696229478399
"nd_hex": "0xffd5bffffffff"
"nd_bit": "2^52 - 2^41 - 2^39 - 2^37 - 2^34 - 1"
"r2": 3114467891909449
"r2_hex": "0xb1097905c9349"
"r2_bit": "2^52 - 2^50 - 2^48 + 2^44 + 2^39 + 2^37 - 2^35 - 2^31 + 2^28 + 2^23 - 2^21 - 2^18 + 2^15 + 2^12 + 2^10 - 2^8 + 2^6 + 2^3 + 1"
"znprimroot": 31
- "n": 4493996080496641
"n_hex": "0xff74400000001"
"n_bit": "2^52 - 2^43 - 2^40 + 2^38 + 2^34 + 1"
"n_fac": "2^34 * 3^2 * 5 * 5813 + 1"
"nd": 4493996080496639
"nd_hex": "0xff743ffffffff"
"nd_bit": "2^52 - 2^43 - 2^40 + 2^38 + 2^34 - 1"
"r2": 3035851340856470
"r2_hex": "0xac91738c33c96"
"r2_bit": "2^52 - 2^50 - 2^48 - 2^46 + 2^43 + 2^40 + 2^37 - 2^35 - 2^32 + 2^30 - 2^27 + 2^24 - 2^22 + 2^18 - 2^16 + 2^14 - 2^10 + 2^7 + 2^5 - 2^3 - 2"
"znprimroot": 41
- "n": 4503084231294977
"n_hex": "0xfff8800000001"
"n_bit": "2^52 - 2^39 + 2^35 + 1"
"n_fac": "2^35 * 83 * 1579 + 1"
"nd": 4503084231294975
"nd_hex": "0xfff87ffffffff"
"nd_bit": "2^52 - 2^39 + 2^35 - 1"
"r2": 3477892658619811
"r2_hex": "0xc5b1ffc7be5a3"
"r2_bit": "2^52 - 2^50 + 2^47 - 2^45 - 2^42 - 2^40 + 2^37 - 2^26 + 2^23 - 2^18 - 2^13 + 2^11 - 2^9 - 2^7 + 2^5 + 2^2 - 1"
"znprimroot": 3
- "n": 4501160085946369
"n_hex": "0xffdc800000001"
"n_bit": "2^52 - 2^41 - 2^38 + 2^35 + 1"
"n_fac": "2^35 * 3 * 13 * 3359 + 1"
"nd": 4501160085946367
"nd_hex": "0xffdc7ffffffff"
"nd_bit": "2^52 - 2^41 - 2^38 + 2^35 - 1"
"r2": 4323587635876432
"r2_hex": "0xf5c47b1311250"
"r2_bit": "2^52 - 2^47 - 2^45 - 2^42 + 2^38 + 2^35 - 2^30 - 2^28 + 2^24 + 2^22 - 2^20 + 2^16 + 2^12 + 2^9 + 2^6 + 2^4"
"znprimroot": 11
- "n": 4500335452225537
"n_hex": "0xffd0800000001"
"n_bit": "2^52 - 2^42 + 2^40 + 2^35 + 1"
"n_fac": "2^35 * 3^5 * 7^2 * 11 + 1"
"nd": 4500335452225535
"nd_hex": "0xffd07ffffffff"
"nd_bit": "2^52 - 2^42 + 2^40 + 2^35 - 1"
"r2": 3320831985963240
"r2_hex": "0xbcc4772e1d0e8"
"r2_bit": "2^52 - 2^50 - 2^46 + 2^44 - 2^42 + 2^38 + 2^35 - 2^31 - 2^28 + 2^26 - 2^24 - 2^21 + 2^17 - 2^14 + 2^12 + 2^8 - 2^5 + 2^3"
"znprimroot": 5
- "n": 4482399668797441
"n_hex": "0xfecb800000001"
"n_bit": "2^52 - 2^44 - 2^42 + 2^40 - 2^38 - 2^35 + 1"
"n_fac": "2^35 * 3^2 * 5 * 13 * 223 + 1"
"nd": 4482399668797439
"nd_hex": "0xfecb7ffffffff"
"nd_bit": "2^52 - 2^44 - 2^42 + 2^40 - 2^38 - 2^35 - 1"
"r2": 1643429098027278
"r2_hex": "0x5d6b0a799f90e"
"r2_bit": "2^51 - 2^49 - 2^45 - 2^43 - 2^40 - 2^38 - 2^36 + 2^31 + 2^29 + 2^27 - 2^23 + 2^21 - 2^19 + 2^17 - 2^11 + 2^8 + 2^4 - 2"
"znprimroot": 11
- "n": 4470030162984961
"n_hex": "0xfe17800000001"
"n_bit": "2^52 - 2^45 + 2^41 - 2^39 - 2^35 + 1"
"n_fac": "2^35 * 3^2 * 5 * 7^2 * 59 + 1"
"nd": 4470030162984959
"nd_hex": "0xfe177ffffffff"
"nd_bit": "2^52 - 2^45 + 2^41 - 2^39 - 2^35 - 1"
"r2": 653716797151222
"r2_hex": "0x2528d4d7a57f6"
"r2_bit": "2^49 + 2^46 + 2^44 + 2^41 + 2^39 + 2^36 - 2^34 + 2^32 + 2^30 + 2^28 - 2^25 - 2^23 - 2^19 + 2^17 + 2^15 - 2^13 - 2^11 - 2^3 - 2"
"znprimroot": 41
- "n": 4449929716039681
"n_hex": "0xfcf3000000001"
"n_bit": "2^52 - 2^46 + 2^44 - 2^40 + 2^38 - 2^36 + 1"
"n_fac": "2^36 * 3^2 * 5 * 1439 + 1"
"nd": 4449929716039679
"nd_hex": "0xfcf2fffffffff"
"nd_bit": "2^52 - 2^46 + 2^44 - 2^40 + 2^38 - 2^36 - 1"
"r2": 3305034404441719
"r2_hex": "0xbbde949a5ae77"
"r2_bit": "2^52 - 2^50 - 2^46 - 2^41 - 2^37 + 2^35 + 2^32 + 2^30 + 2^27 + 2^25 - 2^23 + 2^21 + 2^19 - 2^17 - 2^14 - 2^12 - 2^9 + 2^7 - 2^3 - 1"
"znprimroot": 14
- "n": 4437560210227201
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"n_bit": "2^52 - 2^46 + 2^42 - 2^36 + 1"
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"nd": 4437560210227199
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"r2_bit": "2^52 - 2^47 - 2^45 - 2^42 - 2^40 - 2^36 - 2^34 - 2^32 + 2^30 - 2^28 - 2^26 + 2^24 - 2^20 + 2^18 - 2^14 - 2^8 + 2"
"znprimroot": 13
- "n": 4488893659348993
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"nd": 4488893659348991
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"znprimroot": 13
- "n": 4498376947138561
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"nd": 4498376947138559
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"znprimroot": 13
- "n": 4415913575055361
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"nd": 4415913575055359
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"znprimroot": 19
- "n": 4488756220395521
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"nd": 4488756220395519
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"r2_bit": "2^51 - 2^49 - 2^46 + 2^41 - 2^36 + 2^34 + 2^31 + 2^28 + 2^25 + 2^23 - 2^21 - 2^18 - 2^15 - 2^10 + 2^8 + 2^6 - 2^4 + 2^2 - 1"
"znprimroot": 3
- "n": 4461268429701121
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"nd": 4461268429701119
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"znprimroot": 14
- "n": 4457969894817793
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"nd": 4457969894817791
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"r2": 2488827280297583
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"r2_bit": "2^51 + 2^48 - 2^45 - 2^43 - 2^39 + 2^36 + 2^34 - 2^32 + 2^30 + 2^25 - 2^20 + 2^18 - 2^16 + 2^12 - 2^9 + 2^7 - 2^4 - 1"
"znprimroot": 5
- "n": 4131414941368321
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"nd": 4131414941368319
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"znprimroot": 7
- "n": 4480509883187201
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"nd": 4480509883187199
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"znprimroot": 3
- "n": 4370558720409601
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"znprimroot": 7
- "n": 4126467139043329
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"znprimroot": 7
- "n": 3809807790243841
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"nd": 3809807790243839
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"r2_bit": "2^51 + 2^46 - 2^43 + 2^37 - 2^35 - 2^32 + 2^30 - 2^28 + 2^26 - 2^24 - 2^21 + 2^19 - 2^15 + 2^12 - 2^10 - 2^7 + 2^4 + 2"
"znprimroot": 19
- "n": 3925256511160321
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"nd": 3925256511160319
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"znprimroot": 11
- "n": 3661373720494081
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"nd": 3661373720494079
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"znprimroot": 26
- "n": 3562417673994241
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"nd": 3562417673994239
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"r2_bit": "2^51 - 2^49 + 2^47 + 2^44 - 2^41 - 2^37 - 2^35 + 2^32 - 2^30 + 2^28 - 2^24 + 2^22 + 2^20 + 2^18 + 2^12 + 2^9 - 2^6 - 2^4 + 2^2 + 1"
"znprimroot": 14
- "n": 3799912185593857
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"n_fac": "2^47 * 3^3 + 1"
"nd": 3799912185593855
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"r2": 3388124719665306
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"znprimroot": 5
- "n": 4222124650659841
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"nd": 4222124650659839
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"nd_bit": "2^52 - 2^48 - 1"
"r2": 3921884675501809
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"znprimroot": 19
Raw
result_prime_0058.yaml
- "r": 58
"primes":
- "n": 288230376151711603
"n_hex": "0x3ffffffffffff73"
"n_bit": "2^58 - 2^7 - 2^4 + 2^2 - 1"
"n_fac": "2 * 3^2 * 7 * 2287542667870727 + 1"
"nd": 40883741298115141
"nd_hex": "0x913f8bcd29c245"
"nd_bit": "2^55 + 2^52 + 2^48 + 2^46 - 2^39 + 2^36 - 2^34 - 2^30 + 2^28 - 2^26 + 2^24 + 2^21 + 2^19 + 2^17 - 2^14 + 2^9 + 2^6 + 2^2 + 1"
"r2": 19881
"r2_hex": "0x4da9"
"r2_bit": "2^14 + 2^12 - 2^9 - 2^7 + 2^5 + 2^3 + 1"
"znprimroot": 3
- "n": 288230376151711531
"n_hex": "0x3ffffffffffff2b"
"n_bit": "2^58 - 2^8 + 2^6 - 2^4 - 2^2 - 1"
"n_fac": "2 * 3^2 * 5 * 1523 * 2579 * 815353601 + 1"
"nd": 221923857694275709
"nd_hex": "0x3146e92a10d387d"
"nd_bit": "2^58 - 2^56 + 2^52 + 2^50 + 2^47 - 2^44 - 2^41 + 2^39 + 2^36 + 2^33 + 2^31 + 2^29 + 2^24 + 2^20 - 2^18 + 2^16 + 2^14 - 2^11 + 2^7 - 2^2 + 1"
"r2": 45369
"r2_hex": "0xb139"
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"znprimroot": 10
- "n": 288230376151711351
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"n_bit": "2^58 - 2^9 + 2^7 - 2^3 - 1"
"n_fac": "2 * 3^3 * 5^2 * 7 * 9173 * 3325037491c + 1"
"nd": 93876560171549881
"nd_hex": "0x14d843bedc2c4b9"
"nd_bit": "2^56 + 2^54 + 2^52 - 2^49 - 2^47 + 2^42 + 2^38 - 2^34 - 2^28 - 2^25 - 2^22 + 2^18 - 2^16 - 2^14 + 2^10 + 2^8 - 2^6 - 2^3 + 1"
"r2": 154449
"r2_hex": "0x25b51"
"r2_bit": "2^17 + 2^15 - 2^13 - 2^10 - 2^8 + 2^6 + 2^4 + 1"
"znprimroot": 7
- "n": 288230376151711717
"n_hex": "0x3ffffffffffffe5"
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"n_fac": "2^2 * 3 * 24019198012642643 + 1"
"nd": 53375995583650323
"nd_hex": "0xbda12f684bda13"
"nd_bit": "2^56 - 2^54 - 2^49 - 2^47 + 2^45 + 2^40 + 2^38 - 2^36 - 2^31 - 2^29 + 2^27 + 2^22 + 2^20 - 2^18 - 2^13 - 2^11 + 2^9 + 2^4 + 2^2 - 1"
"r2": 729
"r2_hex": "0x2d9"
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"znprimroot": 6
- "n": 288230376151706941
"n_hex": "0x3ffffffffffed3d"
"n_bit": "2^58 - 2^12 - 2^10 + 2^8 + 2^6 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5 * 7 * 19 * 61 * 1621 * 121759471 + 1"
"nd": 27844866653007339
"nd_hex": "0x62ecc239abadeb"
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"r2_bit": "2^55 - 2^53 - 2^50 + 2^48 - 2^46 + 2^43 - 2^36 - 2^34 + 2^31 - 2^24 - 2^22 + 2^19 - 2^12 - 2^10 + 2^7 + 2^5 - 2^3 - 1"
"znprimroot": 17
- "n": 284852676431183873
"n_hex": "0x3f4000000000001"
"n_bit": "2^58 - 2^52 + 2^50 + 1"
"n_fac": "2^50 * 11 * 23 + 1"
"nd": 284852676431183871
"nd_hex": "0x3f3ffffffffffff"
"nd_bit": "2^58 - 2^52 + 2^50 - 1"
"r2": 201496031549487470
"r2_hex": "0x2cbdb92b828796e"
"r2_bit": "2^58 - 2^56 - 2^54 + 2^52 - 2^50 - 2^45 - 2^42 - 2^39 + 2^36 + 2^34 - 2^32 - 2^30 - 2^27 + 2^21 + 2^19 + 2^15 - 2^11 + 2^9 - 2^7 - 2^4 - 2"
"znprimroot": 3
- "n": 280349076803813377
"n_hex": "0x3e4000000000001"
"n_bit": "2^58 - 2^53 + 2^50 + 1"
"n_fac": "2^50 * 3 * 83 + 1"
"nd": 280349076803813375
"nd_hex": "0x3e3ffffffffffff"
"nd_bit": "2^58 - 2^53 + 2^50 - 1"
"r2": 52695732989333094
"r2_hex": "0xbb367d6e020e66"
"r2_bit": "2^56 - 2^54 - 2^50 - 2^48 + 2^46 - 2^43 - 2^41 + 2^39 - 2^33 - 2^31 - 2^28 - 2^25 + 2^17 + 2^12 - 2^9 + 2^7 - 2^5 + 2^3 - 2"
"znprimroot": 5
- "n": 30399297484750849
"n_hex": "0x6c000000000001"
"n_bit": "2^55 - 2^52 - 2^50 + 1"
"n_fac": "2^50 * 3^3 + 1"
"nd": 30399297484750847
"nd_hex": "0x6bffffffffffff"
"nd_bit": "2^55 - 2^52 - 2^50 - 1"
"r2": 24477897974689731
"r2_hex": "0x56f684bda12fc3"
"r2_bit": "2^55 - 2^53 - 2^51 - 2^48 - 2^43 - 2^41 + 2^39 + 2^34 + 2^32 - 2^30 - 2^25 - 2^23 + 2^21 + 2^16 + 2^14 - 2^12 - 2^6 + 2^2 - 1"
"znprimroot": 11
- "n": 168884986026393601
"n_hex": "0x258000000000001"
"n_bit": "2^57 + 2^55 - 2^53 - 2^51 + 1"
"n_fac": "2^51 * 3 * 5^2 + 1"
"nd": 168884986026393599
"nd_hex": "0x257ffffffffffff"
"nd_bit": "2^57 + 2^55 - 2^53 - 2^51 - 1"
"r2": 86799376818187363
"r2_hex": "0x1345f92c5f92c63"
"r2_bit": "2^56 + 2^54 - 2^52 + 2^50 + 2^47 - 2^45 - 2^39 + 2^36 + 2^34 - 2^32 - 2^30 + 2^27 - 2^25 - 2^19 + 2^16 + 2^14 - 2^12 - 2^10 + 2^7 - 2^5 + 2^2 - 1"
"znprimroot": 11
- "n": 180143985094819841
"n_hex": "0x280000000000001"
"n_bit": "2^57 + 2^55 + 1"
"n_fac": "2^55 * 5 + 1"
"nd": 180143985094819839
"nd_hex": "0x27fffffffffffff"
"nd_bit": "2^57 + 2^55 - 1"
"r2": 151320947479648669
"r2_hex": "0x21999999999999d"
"r2_bit": "2^57 + 2^53 - 2^51 + 2^49 - 2^47 + 2^45 - 2^43 + 2^41 - 2^39 + 2^37 - 2^35 + 2^33 - 2^31 + 2^29 - 2^27 + 2^25 - 2^23 + 2^21 - 2^19 + 2^17 - 2^15 + 2^13 - 2^11 + 2^9 - 2^7 + 2^5 - 2^2 + 1"
"znprimroot": 6
Raw
result_prime_0059.yaml
- "r": 59
"primes":
- "n": 576460752303423061
"n_hex": "0x7fffffffffffe55"
"n_bit": "2^59 - 2^9 + 2^6 + 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5 * 1523 * 2579 * 815353601 + 1"
"nd": 573760701941346563
"nd_hex": "0x7f66851894af103"
"nd_bit": "2^59 - 2^51 - 2^49 + 2^47 - 2^45 + 2^43 + 2^38 + 2^36 + 2^33 - 2^31 + 2^27 + 2^24 + 2^22 + 2^20 - 2^18 - 2^16 - 2^12 + 2^8 + 2^2 - 1"
"r2": 182329
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"r2_bit": "2^18 - 2^16 - 2^14 + 2^11 + 2^6 - 2^3 + 1"
"znprimroot": 2
- "n": 576460752303423433
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"n_bit": "2^59 - 2^6 + 2^3 + 1"
"n_fac": "2^3 * 3 * 24019198012642643 + 1"
"nd": 555498543128753543
"nd_hex": "0x7b586fb586fb587"
"nd_bit": "2^59 - 2^54 - 2^51 - 2^49 - 2^47 + 2^43 - 2^40 - 2^34 - 2^31 - 2^29 - 2^27 + 2^23 - 2^20 - 2^14 - 2^11 - 2^9 - 2^7 + 2^3 - 1"
"r2": 3025
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"znprimroot": 5
- "n": 576460752303422281
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"n_fac": "2^3 * 3 * 5 * 7 * 1061 * 9491 * 68149567 + 1"
"nd": 479985961942784263
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"nd_bit": "2^59 - 2^57 + 2^55 + 2^53 + 2^51 + 2^48 + 2^46 + 2^40 - 2^38 - 2^36 + 2^31 - 2^27 - 2^24 - 2^22 + 2^19 - 2^17 + 2^13 - 2^11 + 2^8 + 2^3 - 1"
"r2": 1456849
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"r2_bit": "2^21 - 2^19 - 2^17 + 2^14 - 2^10 - 2^8 - 2^6 + 2^4 + 1"
"znprimroot": 19
- "n": 576460752303422881
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"nd": 316246178776013215
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"nd_bit": "2^58 + 2^55 - 2^53 + 2^50 - 2^47 + 2^43 + 2^38 - 2^35 + 2^33 - 2^31 - 2^29 - 2^26 - 2^23 + 2^18 + 2^16 - 2^13 - 2^11 + 2^9 - 2^7 + 2^5 - 1"
"r2": 368449
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"znprimroot": 7
- "n": 576460752303421441
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"nd": 540414354504284159
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"r2": 4190209
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"r2_bit": "2^22 - 2^12 + 1"
"znprimroot": 19
- "n": 576460752303419393
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"n_fac": "2^12 * 2351 * 4513 * 13264529 + 1"
"nd": 576179208590454783
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"r2": 16769025
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"znprimroot": 3
- "n": 576460752302665729
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"n_fac": "2^12 * 3^3 * 83 * 62801199623 + 1"
"nd": 402281524624650239
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"nd_bit": "2^59 - 2^57 - 2^55 + 2^52 + 2^50 + 2^48 + 2^46 - 2^44 + 2^40 - 2^37 + 2^35 + 2^33 + 2^30 + 2^28 - 2^24 - 2^20 + 2^18 + 2^15 - 2^12 - 1"
"r2": 574198702081
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"znprimroot": 13
- "n": 576460752301486081
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"n_fac": "2^12 * 3^2 * 5 * 7^2 * 63826525331 + 1"
"nd": 446727202338402303
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"nd_bit": "2^59 - 2^57 + 2^54 - 2^52 + 2^50 - 2^48 + 2^45 - 2^43 + 2^35 - 2^33 + 2^28 - 2^24 - 2^21 + 2^17 + 2^15 - 2^12 - 1"
"r2": 3753545883649
"r2_hex": "0x369f0c4e001"
"r2_bit": "2^42 - 2^39 - 2^37 + 2^35 + 2^33 - 2^28 + 2^24 - 2^22 + 2^18 + 2^16 - 2^13 + 1"
"znprimroot": 34
- "n": 576460752303415297
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"nd": 571956602853122047
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"nd_bit": "2^59 - 2^52 - 2^39 - 2^26 - 2^13 - 1"
"r2": 67092481
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"r2_bit": "2^26 - 2^14 + 1"
"znprimroot": 5
- "n": 576460752302530561
"n_hex": "0x7fffffffff26001"
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"n_fac": "2^13 * 3 * 5 * 541 * 8671441057 + 1"
"nd": 364409791716679679
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"r2": 797318627329
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"znprimroot": 13
- "n": 576460752301449217
"n_hex": "0x7ffffffffe1e001"
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"n_fac": "2^13 * 3^3 * 53 * 193 * 254790281 + 1"
"nd": 82494108947570687
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"r2": 3897745981441
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"znprimroot": 5
- "n": 576460752296878081
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"n_fac": "2^13 * 3^2 * 5 * 1231 * 8269 * 153623 + 1"
"nd": 311075517578878975
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"r2": 42842352795649
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"znprimroot": 7
- "n": 576460752303210497
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"r2": 45365166081
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- "n": 576460752303046657
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"r2": 142001602561
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- "n": 576460752302161921
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- "n": 576460752293314561
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- "n": 576460752289873921
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- "n": 576460752302473217
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- "n": 576460752301228033
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- "n": 576460752297492481
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- "n": 576460752291594241
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"r2_bit": "2^57 - 2^53 + 2^51 - 2^49 + 2^47 - 2^40 + 2^38 - 2^35 + 2^33 - 2^31 - 2^29 + 2^27 - 2^20 + 2^18 - 2^15 + 2^13 - 2^11 - 2^9 + 2^7 + 2"
"znprimroot": 7
- "n": 303992974847508481
"n_hex": "0x438000000000001"
"n_bit": "2^58 + 2^54 - 2^51 + 1"
"n_fac": "2^51 * 3^3 * 5 + 1"
"nd": 303992974847508479
"nd_hex": "0x437ffffffffffff"
"nd_bit": "2^58 + 2^54 - 2^51 - 1"
"r2": 208399902756914734
"r2_hex": "0x2e4629b7f0d462e"
"r2_bit": "2^58 - 2^56 - 2^53 + 2^50 + 2^47 - 2^45 + 2^41 + 2^39 + 2^37 - 2^34 - 2^31 - 2^24 + 2^20 - 2^18 + 2^16 + 2^14 + 2^11 - 2^9 + 2^6 - 2^4 - 2"
"znprimroot": 11
- "n": 459367161991790593
"n_hex": "0x660000000000001"
"n_bit": "2^59 - 2^57 + 2^55 - 2^53 + 1"
"n_fac": "2^53 * 3 * 17 + 1"
"nd": 459367161991790591
"nd_hex": "0x65fffffffffffff"
"nd_bit": "2^59 - 2^57 + 2^55 - 2^53 - 1"
"r2": 213346994112296440
"r2_hex": "0x2f5f5f5f5f5f5f8"
"r2_bit": "2^58 - 2^56 - 2^51 - 2^49 - 2^43 - 2^41 - 2^35 - 2^33 - 2^27 - 2^25 - 2^19 - 2^17 - 2^11 - 2^9 - 2^3"
"znprimroot": 5
- "n": 180143985094819841
"n_hex": "0x280000000000001"
"n_bit": "2^57 + 2^55 + 1"
"n_fac": "2^55 * 5 + 1"
"nd": 180143985094819839
"nd_hex": "0x27fffffffffffff"
"nd_bit": "2^57 + 2^55 - 1"
"r2": 64851834634135153
"r2_hex": "0xe6666666666671"
"r2_bit": "2^56 - 2^53 + 2^51 - 2^49 + 2^47 - 2^45 + 2^43 - 2^41 + 2^39 - 2^37 + 2^35 - 2^33 + 2^31 - 2^29 + 2^27 - 2^25 + 2^23 - 2^21 + 2^19 - 2^17 + 2^15 - 2^13 + 2^11 - 2^9 + 2^7 - 2^4 + 1"
"znprimroot": 6
Raw
result_prime_0060.yaml
- "r": 60
"primes":
- "n": 1152921504606846883
"n_hex": "0xfffffffffffffa3"
"n_bit": "2^60 - 2^7 + 2^5 + 2^2 - 1"
"n_fac": "2 * 3 * 31 * 6198502712940037c + 1"
"nd": 1140524499180966901
"nd_hex": "0xfd3f4fd3f4fd3f5"
"nd_bit": "2^60 - 2^54 + 2^52 + 2^50 - 2^44 + 2^42 + 2^40 - 2^34 + 2^32 + 2^30 - 2^24 + 2^22 + 2^20 - 2^14 + 2^12 + 2^10 - 2^4 + 2^2 + 1"
"r2": 8649
"r2_hex": "0x21c9"
"r2_bit": "2^13 + 2^9 - 2^6 + 2^3 + 1"
"znprimroot": 2
- "n": 1152921504606844591
"n_hex": "0xffffffffffff6af"
"n_bit": "2^60 - 2^11 - 2^8 - 2^6 - 2^4 - 1"
"n_fac": "2 * 3^3 * 5 * 521 * 1777 * 4612228601 + 1"
"nd": 412828077540564913
"nd_hex": "0x5baa8f3031cdfb1"
"nd_bit": "2^59 - 2^57 - 2^54 - 2^51 + 2^49 + 2^47 + 2^45 + 2^43 + 2^40 - 2^36 + 2^34 - 2^32 + 2^26 - 2^24 + 2^21 - 2^18 + 2^16 - 2^13 - 2^6 - 2^4 + 1"
"r2": 5688225
"r2_hex": "0x56cba1"
"r2_bit": "2^23 - 2^21 - 2^19 - 2^16 - 2^14 + 2^12 - 2^10 - 2^7 + 2^5 + 1"
"znprimroot": 15
- "n": 1152921504606841831
"n_hex": "0xfffffffffffebe7"
"n_bit": "2^60 - 2^12 - 2^10 - 2^5 + 2^3 - 1"
"n_fac": "2 * 3 * 5 * 7 * 223 * 24619293286501c + 1"
"nd": 799762264323000361
"nd_hex": "0xb19538ac5bc0829"
"nd_bit": "2^60 - 2^58 - 2^56 + 2^53 - 2^51 + 2^48 + 2^46 + 2^44 + 2^42 - 2^39 + 2^36 - 2^34 - 2^32 - 2^30 + 2^27 - 2^25 - 2^22 - 2^18 + 2^11 + 2^5 + 2^3 + 1"
"r2": 26471025
"r2_hex": "0x193ea71"
"r2_bit": "2^25 - 2^23 + 2^20 + 2^18 - 2^13 + 2^11 + 2^9 + 2^7 - 2^4 + 1"
"znprimroot": 7
- "n": 1152921504606846869
"n_hex": "0xfffffffffffff95"
"n_bit": "2^60 - 2^7 + 2^4 + 2^2 + 1"
"n_fac": "2^2 * 288230376151711717 + 1"
"nd": 549523333971487811
"nd_hex": "0x7a04c8f8d28ac43"
"nd_bit": "2^59 - 2^55 + 2^53 + 2^46 + 2^44 - 2^42 + 2^39 + 2^36 - 2^31 + 2^28 - 2^26 + 2^24 + 2^21 + 2^19 + 2^16 - 2^14 - 2^12 - 2^10 + 2^6 + 2^2 - 1"
"r2": 11449
"r2_hex": "0x2cb9"
"r2_bit": "2^14 - 2^12 - 2^10 + 2^8 - 2^6 - 2^3 + 1"
"znprimroot": 2
- "n": 1152921504606843421
"n_hex": "0xffffffffffff21d"
"n_bit": "2^60 - 2^12 + 2^9 + 2^5 - 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5 * 881 * 7270283166899 + 1"
"nd": 992063820701081547
"nd_hex": "0xdc484c9eb679fcb"
"nd_bit": "2^60 - 2^57 - 2^54 + 2^50 + 2^47 + 2^42 + 2^40 - 2^38 + 2^35 + 2^33 - 2^28 - 2^26 - 2^23 - 2^21 + 2^19 - 2^15 + 2^13 - 2^6 + 2^4 - 2^2 - 1"
"r2": 12638025
"r2_hex": "0xc0d749"
"r2_bit": "2^24 - 2^22 + 2^16 - 2^13 - 2^11 - 2^8 + 2^6 + 2^3 + 1"
"znprimroot": 2
- "n": 1152921504606846697
"n_hex": "0xffffffffffffee9"
"n_bit": "2^60 - 2^8 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3^3 * 31 * 172180630915001c + 1"
"nd": 1148789169464886951
"nd_hex": "0xff151a9bfc546a7"
"nd_bit": "2^60 - 2^52 + 2^48 + 2^46 + 2^44 + 2^41 - 2^39 + 2^37 + 2^35 + 2^33 - 2^30 - 2^22 + 2^18 + 2^16 + 2^14 + 2^11 - 2^9 + 2^7 + 2^5 + 2^3 - 1"
"r2": 77841
"r2_hex": "0x13011"
"r2_bit": "2^16 + 2^14 - 2^12 + 2^4 + 1"
"znprimroot": 11
- "n": 1152921504606845161
"n_hex": "0xffffffffffff8e9"
"n_bit": "2^60 - 2^11 + 2^8 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 5 * 11 * 73 * 11964731264081c + 1"
"nd": 208986873286860967
"nd_hex": "0x2e6787438fba0a7"
"nd_bit": "2^58 - 2^56 - 2^53 + 2^51 - 2^49 + 2^47 - 2^43 + 2^39 - 2^36 + 2^34 + 2^30 - 2^27 + 2^24 - 2^18 - 2^15 + 2^13 + 2^7 + 2^5 + 2^3 - 1"
"r2": 3294225
"r2_hex": "0x324411"
"r2_bit": "2^22 - 2^20 + 2^17 + 2^14 + 2^10 + 2^4 + 1"
"znprimroot": 7
- "n": 1152921504606830281
"n_hex": "0xfffffffffffbec9"
"n_bit": "2^60 - 2^14 - 2^8 - 2^6 + 2^3 + 1"
"n_fac": "2^3 * 3^3 * 5 * 7 * 152502844524713c + 1"
"nd": 717787727995421831
"nd_hex": "0x9f61822b74d4487"
"nd_bit": "2^59 + 2^57 - 2^51 - 2^49 + 2^45 - 2^43 + 2^37 + 2^34 - 2^32 - 2^30 - 2^27 - 2^24 + 2^22 + 2^20 - 2^18 + 2^16 + 2^14 + 2^10 + 2^7 + 2^3 - 1"
"r2": 278723025
"r2_hex": "0x109cf9d1"
"r2_bit": "2^28 + 2^23 + 2^21 - 2^18 + 2^16 - 2^11 + 2^9 - 2^6 + 2^4 + 1"
"znprimroot": 26
- "n": 1152921504606846577
"n_hex": "0xffffffffffffe71"
"n_bit": "2^60 - 2^9 + 2^7 - 2^4 + 1"
"n_fac": "2^4 * 3 * 7 * 23 * 71 * 2101233314027c + 1"
"nd": 846631581077208431
"nd_hex": "0xbbfd6eff5bbfd6f"
"nd_bit": "2^60 - 2^58 - 2^54 - 2^45 - 2^43 - 2^40 - 2^36 - 2^27 - 2^25 - 2^22 - 2^18 - 2^9 - 2^7 - 2^4 - 1"
"r2": 159201
"r2_hex": "0x26de1"
"r2_bit": "2^17 + 2^15 - 2^12 - 2^9 - 2^5 + 1"
"znprimroot": 15
- "n": 1152921504606845473
"n_hex": "0xffffffffffffa21"
"n_bit": "2^60 - 2^11 + 2^9 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 23 * 174052159511903 + 1"
"nd": 744834850946938399
"nd_hex": "0xa562f59c305f61f"
"nd_bit": "2^59 + 2^57 + 2^55 - 2^53 - 2^51 - 2^49 + 2^46 - 2^44 - 2^39 - 2^37 - 2^35 + 2^33 - 2^30 + 2^26 - 2^24 + 2^19 - 2^17 - 2^11 - 2^9 + 2^5 - 1"
"r2": 2259009
"r2_hex": "0x227841"
"r2_bit": "2^21 + 2^17 + 2^15 - 2^11 + 2^6 + 1"
"znprimroot": 7
- "n": 1152921504606841441
"n_hex": "0xfffffffffffea61"
"n_bit": "2^60 - 2^13 + 2^11 + 2^9 + 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 19 * 41 * 1027779119069c + 1"
"nd": 384098871634151007
"nd_hex": "0x55497e38261c65f"
"nd_bit": "2^58 + 2^56 + 2^54 + 2^52 + 2^50 + 2^47 + 2^45 - 2^43 - 2^37 + 2^34 - 2^31 + 2^25 + 2^23 - 2^21 + 2^17 - 2^14 + 2^11 - 2^9 + 2^7 - 2^5 - 1"
"r2": 30636225
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"r2_bit": "2^25 - 2^22 + 2^20 + 2^18 - 2^15 - 2^11 + 2^8 - 2^6 + 1"
"znprimroot": 7
- "n": 1152921504606732001
"n_hex": "0xffffffffffe3ee1"
"n_bit": "2^60 - 2^17 + 2^14 - 2^8 - 2^5 + 1"
"n_fac": "2^5 * 3^3 * 5^3 * 7 * 19^2 * 4224455527c + 1"
"nd": 189511315638745823
"nd_hex": "0x2a1478999907adf"
"nd_bit": "2^57 + 2^55 + 2^53 + 2^48 + 2^46 + 2^43 - 2^39 + 2^35 + 2^33 - 2^31 + 2^29 - 2^27 + 2^25 - 2^23 + 2^20 + 2^15 - 2^10 - 2^8 - 2^5 - 1"
"r2": 13219250625
"r2_hex": "0x313edc1c1"
"r2_bit": "2^34 - 2^32 + 2^28 + 2^26 - 2^20 - 2^17 - 2^14 + 2^9 - 2^6 + 1"
"znprimroot": 13
- "n": 1152921504606836161
"n_hex": "0xfffffffffffd5c1"
"n_bit": "2^60 - 2^13 - 2^11 - 2^9 - 2^6 + 1"
"n_fac": "2^6 * 3 * 5 * 7 * 171565700090303c + 1"
"nd": 391662839382853055
"nd_hex": "0x56f7746fd22c5bf"
"nd_bit": "2^59 - 2^57 - 2^55 - 2^52 - 2^47 - 2^43 - 2^40 + 2^38 + 2^35 - 2^32 - 2^26 + 2^24 + 2^21 + 2^18 - 2^16 - 2^14 + 2^11 - 2^9 - 2^6 - 1"
"r2": 116964225
"r2_hex": "0x6f8bb81"
"r2_bit": "2^27 - 2^24 - 2^19 + 2^16 - 2^14 - 2^10 - 2^7 + 1"
"znprimroot": 19
- "n": 1152921504606833089
"n_hex": "0xfffffffffffc9c1"
"n_bit": "2^60 - 2^14 + 2^11 + 2^9 - 2^6 + 1"
"n_fac": "2^6 * 3^3 * 17 * 109 * 360064730057c + 1"
"nd": 593936807370734015
"nd_hex": "0x83e1661265cb9bf"
"nd_bit": "2^59 + 2^54 - 2^49 + 2^45 - 2^43 - 2^41 + 2^39 - 2^37 + 2^32 + 2^29 + 2^27 - 2^25 + 2^23 - 2^21 - 2^18 + 2^16 - 2^14 - 2^11 + 2^9 - 2^6 - 1"
"r2": 192848769
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"r2_bit": "2^28 - 2^26 - 2^23 - 2^17 + 2^15 + 2^13 + 2^10 - 2^7 + 1"
"znprimroot": 11
- "n": 1152921504606759361
"n_hex": "0xffffffffffea9c1"
"n_bit": "2^60 - 2^17 + 2^15 + 2^13 + 2^11 + 2^9 - 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 11 * 19 * 23 * 83278545221c + 1"
"nd": 280075116179331519
"nd_hex": "0x3e306d5924b99bf"
"nd_bit": "2^58 - 2^53 + 2^50 - 2^48 + 2^43 - 2^40 - 2^37 - 2^35 - 2^33 - 2^31 + 2^28 + 2^25 + 2^22 + 2^20 - 2^18 - 2^15 + 2^13 - 2^11 + 2^9 - 2^6 - 1"
"r2": 7676388225
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"r2_bit": "2^33 - 2^30 + 2^27 + 2^25 - 2^23 + 2^20 - 2^18 + 2^15 - 2^13 + 2^10 - 2^7 + 1"
"znprimroot": 13
- "n": 1152921504606701761
"n_hex": "0xffffffffffdc8c1"
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"n_fac": "2^6 * 3^5 * 5 * 7 * 2118095062843 + 1"
"nd": 697747157737617599
"nd_hex": "0x9aee557d7fd38bf"
"nd_bit": "2^59 + 2^57 - 2^54 - 2^52 - 2^48 - 2^45 + 2^43 - 2^41 - 2^39 - 2^37 - 2^35 - 2^29 - 2^27 - 2^18 + 2^16 + 2^14 - 2^11 + 2^8 - 2^6 - 1"
"r2": 21087396225
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"znprimroot": 11
- "n": 1152921504606830209
"n_hex": "0xfffffffffffbe81"
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"n_fac": "2^7 * 3^2 * 823 * 1216038781523c + 1"
"nd": 522242430219419263
"nd_hex": "0x73f60b92bdd7e7f"
"nd_bit": "2^59 - 2^56 + 2^54 - 2^47 - 2^45 + 2^40 - 2^38 - 2^35 + 2^32 + 2^30 - 2^28 - 2^26 - 2^21 - 2^17 - 2^15 - 2^9 + 2^7 - 1"
"r2": 281132289
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"r2_bit": "2^28 + 2^24 - 2^22 + 2^17 - 2^14 - 2^10 + 2^8 + 1"
"znprimroot": 21
- "n": 1152921504606668161
"n_hex": "0xffffffffffd4581"
"n_bit": "2^60 - 2^18 + 2^16 + 2^14 + 2^11 - 2^9 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 7 * 13 * 19 * 47 * 1553 * 4758107 + 1"
"nd": 466442710786442623
"nd_hex": "0x679232c947f057f"
"nd_bit": "2^59 - 2^57 + 2^55 - 2^51 + 2^48 + 2^45 + 2^42 - 2^40 + 2^38 - 2^36 - 2^34 + 2^31 + 2^28 + 2^26 + 2^23 - 2^16 + 2^11 - 2^9 - 2^7 - 1"
"r2": 31974804225
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"r2_bit": "2^35 - 2^31 - 2^28 + 2^25 - 2^21 - 2^19 + 2^16 - 2^14 + 2^12 - 2^10 - 2^8 + 1"
"znprimroot": 22
- "n": 1152921504606076801
"n_hex": "0xffffffffff43f81"
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"n_fac": "2^7 * 3^2 * 5^2 * 7^2 * 816979524239 + 1"
"nd": 978449268707950463
"nd_hex": "0xd94266d0413ff7f"
"nd_bit": "2^60 - 2^57 - 2^55 + 2^52 + 2^50 + 2^45 + 2^43 - 2^41 + 2^39 - 2^36 - 2^34 + 2^32 + 2^26 + 2^20 + 2^18 - 2^7 - 1"
"r2": 593169530625
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"znprimroot": 31
- "n": 1152921504606823681
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"nd": 243452280796783871
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"r2": 542657025
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- "n": 1152921504606716161
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"nd": 348207588774314239
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"r2": 17112564225
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"znprimroot": 13
- "n": 1152921504603859201
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"nd": 573725444562577663
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"r2": 8926799450625
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"znprimroot": 33
- "n": 1152921504606844417
"n_hex": "0xffffffffffff601"
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"nd": 880797788787176959
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"nd_bit": "2^60 - 2^58 + 2^54 - 2^51 + 2^48 + 2^46 - 2^43 + 2^40 - 2^36 - 2^34 + 2^29 - 2^27 - 2^23 + 2^21 - 2^18 - 2^11 - 2^9 - 1"
"r2": 6548481
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"znprimroot": 10
- "n": 1152921504606574081
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"n_fac": "2^9 * 3 * 5 * 7 * 647 * 33146387189 + 1"
"nd": 450695370710177279
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"r2": 74471681025
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"znprimroot": 26
- "n": 1152921504602488321
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"n_fac": "2^9 * 3^2 * 5 * 7 * 127 * 1427 * 39444961 + 1"
"nd": 1022939484858711551
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"r2": 18997873409025
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"znprimroot": 22
- "n": 1152921504606815233
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"n_fac": "2^10 * 3^2 * 125099989649177 + 1"
"nd": 1111370857180005375
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"r2": 1007618049
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"znprimroot": 3
- "n": 1137440380887760897
"n_hex": "0xfc9000000000001"
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"nd": 1137440380887760895
"nd_hex": "0xfc8ffffffffffff"
"nd_bit": "2^60 - 2^54 + 2^51 + 2^48 - 1"
"r2": 181903604214261710
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"r2_bit": "2^57 + 2^55 + 2^51 - 2^49 + 2^46 + 2^39 - 2^37 - 2^34 + 2^32 + 2^30 + 2^23 + 2^20 - 2^17 - 2^13 + 2^11 - 2^6 + 2^4 - 2"
"znprimroot": 7
- "n": 1076641785918259201
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"n_bit": "2^60 - 2^56 - 2^52 + 2^48 + 1"
"n_fac": "2^48 * 3^2 * 5^2 * 17 + 1"
"nd": 1076641785918259199
"nd_hex": "0xef0ffffffffffff"
"nd_bit": "2^60 - 2^56 - 2^52 + 2^48 - 1"
"r2": 488302716009416825
"r2_hex": "0x6c6ccbbaa998879"
"r2_bit": "2^59 - 2^56 - 2^54 + 2^51 - 2^48 - 2^46 + 2^44 - 2^42 + 2^40 - 2^38 - 2^34 - 2^31 + 2^29 + 2^27 + 2^25 + 2^23 + 2^21 - 2^19 + 2^17 - 2^15 + 2^11 + 2^7 - 2^3 + 1"
"znprimroot": 19
- "n": 857091304083947521
"n_hex": "0xbe5000000000001"
"n_bit": "2^60 - 2^58 - 2^53 + 2^50 + 2^48 + 1"
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"nd": 857091304083947519
"nd_hex": "0xbe4ffffffffffff"
"nd_bit": "2^60 - 2^58 - 2^53 + 2^50 + 2^48 - 1"
"r2": 488708409367040566
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"r2_bit": "2^59 - 2^56 - 2^54 + 2^51 + 2^46 - 2^41 - 2^38 - 2^35 - 2^33 - 2^31 + 2^26 - 2^24 + 2^20 + 2^17 - 2^15 + 2^12 + 2^9 + 2^6 - 2^3 - 2"
"znprimroot": 11
- "n": 265993852991569921
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"nd": 265993852991569919
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"r2_bit": "2^56 - 2^54 + 2^51 + 2^49 + 2^46 + 2^44 + 2^42 + 2^40 + 2^36 - 2^26 - 2^23 + 2^21 + 2^19 + 2^17 + 2^15 - 2^13 + 2^11 - 2^9 - 2^7 - 2^5 + 2^2"
"znprimroot": 17
- "n": 1102818958752350209
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"znprimroot": 7
- "n": 1055531162664960001
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"znprimroot": 13
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"nd": 937311672446484479
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"znprimroot": 7
- "n": 59109745109237761
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"nd": 59109745109237759
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"znprimroot": 17
- "n": 1043709213643112449
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"nd": 1043709213643112447
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"znprimroot": 7
- "n": 861313428734607361
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"nd": 861313428734607359
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"znprimroot": 13
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"znprimroot": 3
- "n": 1033576114481528833
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"znprimroot": 7
- "n": 979532918953082881
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"znprimroot": 11
- "n": 303992974847508481
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"znprimroot": 11
- "n": 1139410705724735489
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"nd": 1139410705724735487
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"znprimroot": 3
- "n": 1067353111686807553
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"nd": 1067353111686807551
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"znprimroot": 5
- "n": 891712726219358209
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"znprimroot": 7
- "n": 882705526964617217
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"znprimroot": 5
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"znprimroot": 6
Raw
result_prime_0061.yaml
- "r": 61
"primes":
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"n_hex": "0x1fffffffffffffff"
"n_bit": "2^61 - 1"
"n_fac": "2 * 3^2 * 5^2 * 7 * 11 * 13 * 31 * 41 * 61 * 151 * 331 * 1321 + 1"
"nd": 1
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- "n": 2305843009213692601
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"nd": 172383526225450103
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"nd_bit": "2^57 + 2^55 - 2^53 + 2^50 + 2^47 - 2^44 - 2^41 - 2^37 + 2^35 - 2^31 - 2^29 - 2^25 - 2^22 + 2^20 - 2^18 + 2^12 + 2^10 + 2^7 - 2^3 - 1"
"r2": 1825201
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- "n": 2305843009213690801
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"nd": 1811158821899045551
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"r2": 9928801
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- "n": 2305843009213693921
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"r2": 961
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- "n": 2305843009213675681
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- "n": 2305843009213692737
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"r2": 1476225
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- "n": 2305843009213692097
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"r2": 3441025
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- "n": 2305843009213423681
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"nd": 461542285751865407
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"r2": 73046413441
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"znprimroot": 19
- "n": 2305843009213672321
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"nd": 2193274463250508671
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"r2": 467900161
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"r2_bit": "2^29 - 2^26 - 2^21 + 2^18 - 2^15 + 2^13 - 2^11 - 2^8 + 1"
"znprimroot": 22
- "n": 2305843009213656961
"n_hex": "0x1fffffffffff6f81"
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"n_fac": "2^7 * 3^2 * 5 * 400319966877371c + 1"
"nd": 317722738448871295
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"nd_bit": "2^58 + 2^55 - 2^53 + 2^51 + 2^48 - 2^46 + 2^43 - 2^40 + 2^37 + 2^35 - 2^33 - 2^30 - 2^28 + 2^25 + 2^22 + 2^20 - 2^16 + 2^14 - 2^12 - 2^7 - 1"
"r2": 1368334081
"r2_hex": "0x518f1f01"
"r2_bit": "2^30 + 2^28 + 2^25 - 2^23 + 2^20 - 2^16 + 2^13 - 2^8 + 1"
"znprimroot": 7
- "n": 2305843009213000321
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"nd": 1323054596188744319
"nd_hex": "0x125c6f2538472a7f"
"nd_bit": "2^60 + 2^57 + 2^55 - 2^53 - 2^50 + 2^47 - 2^44 - 2^40 + 2^37 + 2^34 + 2^32 + 2^30 - 2^27 + 2^22 + 2^19 - 2^16 + 2^13 + 2^11 + 2^9 + 2^7 - 1"
"r2": 481123964161
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"znprimroot": 46
- "n": 2305843009213689601
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"r2_bit": "2^61 - 2^57 + 2^54 + 2^51 + 2^47 - 2^43 - 2^32 - 2^30 - 2^28 - 2^25 - 2^18 - 2^14 - 2^11 - 2^9 - 2^7 - 2^4 + 2^2"
"znprimroot": 7
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"nd_hex": "0x1ffab7ffffffffff"
"nd_bit": "2^61 - 2^50 - 2^48 - 2^46 - 2^43 - 1"
"r2": 2216614482630053535
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"r2_bit": "2^61 - 2^56 - 2^54 + 2^50 - 2^48 - 2^40 + 2^37 + 2^32 - 2^30 - 2^27 + 2^24 + 2^21 + 2^19 - 2^17 + 2^15 + 2^12 - 2^9 + 2^7 + 2^5 - 1"
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"znprimroot": 17
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"nd": 2296967751354286079
"nd_hex": "0x1fe077ffffffffff"
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"znprimroot": 29
- "n": 2305543942050938881
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"r2_bit": "2^60 + 2^58 - 2^56 - 2^52 + 2^49 + 2^47 + 2^45 - 2^35 - 2^32 - 2^27 - 2^22 - 2^20 + 2^18 - 2^16 + 2^14 - 2^11 + 2^9 - 2^7 - 2^4 + 2^2 + 1"
"znprimroot": 7
- "n": 2304963399911473153
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"nd": 2304963399911473151
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"r2_bit": "2^61 - 2^59 + 2^54 - 2^49 - 2^47 - 2^38 - 2^36 + 2^33 - 2^29 - 2^27 + 2^23 - 2^21 - 2^17 + 2^13 + 2^8 + 2^6 - 2^4 + 2^2 - 1"
"znprimroot": 5
- "n": 2249864673220362241
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"n_bit": "2^61 - 2^56 + 2^54 - 2^51 + 2^48 + 2^45 + 1"
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"nd": 2249864673220362239
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"r2_bit": "2^53 + 2^49 + 2^47 - 2^44 - 2^42 + 2^40 + 2^38 + 2^35 - 2^33 - 2^31 - 2^29 - 2^27 + 2^25 + 2^17 + 2^15 - 2^13 + 2^10 + 2^8 - 2^5 + 2"
"znprimroot": 19
- "n": 2301972728283922433
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"nd": 2301972728283922431
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"r2_bit": "2^61 - 2^59 - 2^57 - 2^54 + 2^52 + 2^49 - 2^46 - 2^43 + 2^41 + 2^36 + 2^34 + 2^32 - 2^28 + 2^26 + 2^24 + 2^16 + 2^14 + 2^11 - 2^9 + 2^7 + 2^4 - 2"
"znprimroot": 3
- "n": 2297891341121617921
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"nd": 2297891341121617919
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"r2_bit": "2^60 + 2^56 + 2^54 - 2^51 + 2^49 - 2^45 + 2^43 - 2^40 - 2^35 + 2^33 - 2^31 - 2^29 + 2^27 + 2^22 - 2^20 - 2^17 - 2^11 + 2^7 + 2^5 - 2^3 - 1"
"znprimroot": 29
- "n": 2295780278796288001
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"nd": 2295780278796287999
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"r2_bit": "2^58 + 2^55 + 2^53 - 2^50 + 2^48 + 2^45 - 2^43 - 2^37 + 2^34 - 2^32 - 2^30 - 2^28 - 2^24 + 2^22 - 2^14 + 2^11 + 2^8 + 2^6 + 2^2"
"znprimroot": 17
- "n": 2290502622982963201
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"nd": 2290502622982963199
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"r2_bit": "2^61 - 2^54 + 2^51 + 2^48 + 2^45 + 2^41 + 2^39 + 2^36 - 2^32 - 2^29 - 2^26 - 2^24 + 2^22 + 2^20 - 2^17 - 2^15"
"znprimroot": 22
- "n": 2172283132764487681
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- "n": 2300494984656191489
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"znprimroot": 7
- "n": 1980176461159464961
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"znprimroot": 19
- "n": 2299650559726059521
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"znprimroot": 3
- "n": 1967510087207485441
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"nd": 1967510087207485439
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- "n": 2276569611635785729
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- "n": 303992974847508481
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- "n": 2287828610704211969
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- "n": 2053641430080946177
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"znprimroot": 7
- "n": 1945555039024054273
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"znprimroot": 5
Raw
result_prime_0062.yaml
- "r": 62
"primes":
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"n_hex": "0x3fffffffffffffc7"
"n_bit": "2^62 - 2^6 + 2^3 - 1"
"n_fac": "2 * 3^2 * 1289 * 198762435067123 + 1"
"nd": 161813544506224137
"nd_hex": "0x23ee08fb823ee09"
"nd_bit": "2^57 + 2^54 - 2^48 - 2^45 + 2^39 + 2^36 - 2^30 - 2^27 + 2^21 + 2^18 - 2^12 - 2^9 + 2^3 + 1"
"r2": 3249
"r2_hex": "0xcb1"
"r2_bit": "2^12 - 2^10 + 2^8 - 2^6 - 2^4 + 1"
"znprimroot": 6
- "n": 4611686018427387751
"n_hex": "0x3fffffffffffff67"
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"n_fac": "2 * 3 * 5^3 * 6148914691236517 + 1"
"nd": 1416661718079001513
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"nd_bit": "2^60 + 2^58 - 2^55 + 2^53 + 2^51 + 2^48 - 2^41 + 2^38 + 2^36 + 2^34 - 2^31 + 2^29 + 2^27 + 2^24 - 2^17 + 2^14 + 2^12 + 2^10 - 2^7 + 2^5 + 2^3 + 1"
"r2": 23409
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"znprimroot": 3
- "n": 4611686018427387631
"n_hex": "0x3ffffffffffffeef"
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"n_fac": "2 * 3^2 * 5 * 51240955760304307c + 1"
"nd": 1148698348912316401
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"nd_bit": "2^60 - 2^52 + 2^48 - 2^40 + 2^36 - 2^28 + 2^24 - 2^16 + 2^12 - 2^4 + 1"
"r2": 74529
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"znprimroot": 3
- "n": 4611686018427387271
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"n_fac": "2 * 3^3 * 5 * 7 * 23 * 1171 * 90596870471 + 1"
"nd": 3096313677459146697
"nd_hex": "0x2af850e27a22c7c9"
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"r2": 400689
"r2_hex": "0x61d31"
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"znprimroot": 7
- "n": 4611686018427387421
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"n_fac": "2^2 * 3 * 5 * 19 * 37 * 89 * 191 * 4211 * 1527371 + 1"
"nd": 4458917951564368843
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"nd_bit": "2^62 - 2^57 - 2^53 + 2^48 + 2^46 + 2^41 + 2^38 + 2^31 + 2^29 + 2^27 + 2^25 - 2^23 + 2^21 - 2^18 - 2^16 + 2^14 + 2^12 - 2^10 - 2^6 + 2^4 - 2^2 - 1"
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"r2_bit": "2^61 - 2^57 - 2^54 - 2^51 + 2^46 + 2^43 - 2^41 - 2^39 - 2^33 + 2^30 - 2^27 - 2^25 + 2^21 + 2^19 + 2^17 - 2^13 + 2^11 - 2^9 + 2^7 - 2^4 + 2^2 + 1"
"znprimroot": 7
- "n": 4134304457926115329
"n_hex": "0x3960000000000001"
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"n_fac": "2^53 * 3^3 * 17 + 1"
"nd": 4134304457926115327
"nd_hex": "0x395fffffffffffff"
"nd_bit": "2^62 - 2^59 + 2^57 - 2^55 - 2^53 - 1"
"r2": 1061770218031091187
"r2_hex": "0xebc2a6346d50df3"
"r2_bit": "2^60 - 2^56 - 2^54 - 2^50 + 2^45 + 2^43 + 2^41 + 2^39 - 2^37 + 2^34 - 2^32 + 2^30 + 2^27 - 2^24 - 2^22 + 2^20 + 2^18 + 2^16 + 2^12 - 2^9 - 2^4 + 2^2 - 1"
"znprimroot": 7
- "n": 3377699720527872001
"n_hex": "0x2ee0000000000001"
"n_bit": "2^62 - 2^60 - 2^56 - 2^53 + 1"
"n_fac": "2^53 * 3 * 5^3 + 1"
"nd": 3377699720527871999
"nd_hex": "0x2edfffffffffffff"
"nd_bit": "2^62 - 2^60 - 2^56 - 2^53 - 1"
"r2": 1341616324194167600
"r2_hex": "0x129e60f04c756b30"
"r2_bit": "2^60 + 2^57 + 2^55 + 2^53 - 2^49 + 2^47 - 2^45 + 2^40 - 2^36 + 2^30 + 2^28 - 2^26 + 2^23 - 2^19 - 2^17 - 2^15 - 2^12 - 2^10 - 2^8 + 2^6 - 2^4"
"znprimroot": 26
- "n": 3188548536178311169
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"n_bit": "2^62 - 2^60 - 2^58 + 2^54 + 1"
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"nd": 3188548536178311167
"nd_hex": "0x2c3fffffffffffff"
"nd_bit": "2^62 - 2^60 - 2^58 + 2^54 - 1"
"r2": 157447878498127851
"r2_hex": "0x22f5e02e4850feb"
"r2_bit": "2^57 + 2^54 - 2^52 - 2^47 - 2^45 - 2^41 + 2^34 - 2^32 - 2^29 + 2^26 + 2^23 + 2^18 + 2^16 + 2^12 - 2^4 - 2^2 - 1"
"znprimroot": 7
- "n": 2485986994308513793
"n_hex": "0x2280000000000001"
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"n_fac": "2^55 * 3 * 23 + 1"
"nd": 2485986994308513791
"nd_hex": "0x227fffffffffffff"
"nd_bit": "2^61 + 2^57 + 2^55 - 1"
"r2": 1677166609056699500
"r2_hex": "0x17467e2519f8946c"
"r2_bit": "2^61 - 2^59 - 2^56 + 2^54 + 2^51 - 2^49 + 2^47 - 2^41 + 2^37 + 2^34 + 2^32 + 2^29 - 2^27 + 2^25 - 2^19 + 2^15 + 2^12 + 2^10 + 2^7 - 2^4 - 2^2"
"znprimroot": 5
- "n": 1945555039024054273
"n_hex": "0x1b00000000000001"
"n_bit": "2^61 - 2^58 - 2^56 + 1"
"n_fac": "2^56 * 3^3 + 1"
"nd": 1945555039024054271
"nd_hex": "0x1affffffffffffff"
"nd_bit": "2^61 - 2^58 - 2^56 - 1"
"r2": 381638368423099815
"r2_hex": "0x54bda12f684bda7"
"r2_bit": "2^58 + 2^56 + 2^54 + 2^52 - 2^50 - 2^45 - 2^43 + 2^41 + 2^36 + 2^34 - 2^32 - 2^27 - 2^25 + 2^23 + 2^18 + 2^16 - 2^14 - 2^9 - 2^7 + 2^5 + 2^3 - 1"
"znprimroot": 5
- "n": 4179340454199820289
"n_hex": "0x3a00000000000001"
"n_bit": "2^62 - 2^59 + 2^57 + 1"
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"nd": 4179340454199820287
"nd_hex": "0x39ffffffffffffff"
"nd_bit": "2^62 - 2^59 + 2^57 - 1"
"r2": 1684656853714315195
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"r2_bit": "2^61 - 2^59 - 2^55 - 2^53 + 2^48 + 2^45 - 2^43 + 2^41 + 2^39 - 2^34 - 2^31 + 2^29 - 2^27 - 2^25 + 2^20 + 2^17 - 2^15 + 2^13 + 2^11 - 2^6 - 2^2 - 1"
"znprimroot": 3
Raw
result_prime_0063.yaml
- "r": 63
"primes":
- "n": 9223372036854775783
"n_hex": "0x7fffffffffffffe7"
"n_bit": "2^63 - 2^5 + 2^3 - 1"
"n_fac": "2 * 3^4 * 17 * 23 * 145612264166821c + 1"
"nd": 1106804644422573097
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"nd_bit": "2^60 - 2^55 - 2^53 - 2^50 + 2^45 + 2^43 + 2^40 - 2^35 - 2^33 - 2^30 + 2^25 + 2^23 + 2^20 - 2^15 - 2^13 - 2^10 + 2^5 + 2^3 + 1"
"r2": 625
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"r2_bit": "2^9 + 2^7 - 2^4 + 1"
"znprimroot": 3
- "n": 9223372036854775351
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"n_bit": "2^63 - 2^9 + 2^6 - 2^3 - 1"
"n_fac": "2 * 3^3 * 5^2 * 53 * 128908064805797 + 1"
"nd": 686202733595322489
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"nd_bit": "2^59 + 2^57 - 2^55 + 2^51 - 2^49 - 2^45 + 2^41 - 2^38 + 2^29 + 2^26 - 2^21 - 2^19 + 2^17 - 2^13 + 2^11 + 2^7 - 2^3 + 1"
"r2": 208849
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"znprimroot": 3
- "n": 9223372036854765091
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"nd": 7174211934237324917
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"r2": 114854089
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"znprimroot": 3
- "n": 9223372036854775549
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"r2": 67081
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"znprimroot": 2
- "n": 9223372036854751861
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"nd": 2035173418079117859
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"r2": 573458809
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"znprimroot": 6
- "n": 9223372036854775433
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"nd": 688678445418489927
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"r2": 140625
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- "n": 9223372036854775417
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"nd": 353837801925375031
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"r2": 152881
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"znprimroot": 10
- "n": 9223372036854774937
"n_hex": "0x7ffffffffffffc99"
"n_bit": "2^63 - 2^10 + 2^7 + 2^5 - 2^3 + 1"
"n_fac": "2^3 * 3^2 * 128102389400760763c + 1"
"nd": 5591206010860300375
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"nd_bit": "2^62 + 2^60 - 2^57 - 2^55 + 2^53 - 2^51 - 2^44 + 2^42 + 2^38 - 2^33 + 2^30 + 2^28 - 2^23 - 2^21 - 2^18 - 2^15 - 2^13 + 2^11 + 2^7 - 2^5 - 2^3 - 1"
"r2": 758641
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"znprimroot": 5
- "n": 9223372036854750601
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"nd": 1810498862949078855
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"r2": 635392849
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"znprimroot": 13
- "n": 9223372036854775057
"n_hex": "0x7ffffffffffffd11"
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"nd": 73688724661955599
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"r2": 564001
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"znprimroot": 5
- "n": 9223372036854775073
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"nd": 6751257354867849503
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"nd_bit": "2^63 - 2^61 - 2^57 - 2^54 - 2^52 + 2^48 + 2^46 + 2^43 + 2^40 - 2^38 + 2^36 - 2^34 - 2^31 - 2^29 + 2^27 + 2^21 + 2^18 + 2^14 - 2^11 + 2^8 + 2^5 - 1"
"r2": 540225
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"znprimroot": 5
- "n": 9223372036854732961
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"nd": 448823271100478623
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"r2": 3441025
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- "n": 9223372036854772801
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"r2": 9042049
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"r2": 15737089
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- "n": 9223372036854771457
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"r2": 18931201
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"r2": 451435009
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- "n": 9223372036854747649
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- "n": 9223372036854420481
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"nd_bit": "2^63 - 2^58 - 2^56 + 2^54 + 2^51 - 1"
"r2": 405819990300630441
"r2_hex": "0x5a1c3218c9f1da9"
"r2_bit": "2^59 - 2^57 - 2^55 + 2^53 + 2^49 - 2^46 + 2^42 - 2^40 + 2^37 + 2^33 - 2^31 + 2^28 - 2^26 + 2^23 + 2^21 - 2^16 + 2^13 - 2^9 - 2^7 + 2^5 + 2^3 + 1"
"znprimroot": 14
- "n": 7903817346035220481
"n_hex": "0x6db0000000000001"
"n_bit": "2^63 - 2^60 - 2^57 - 2^54 - 2^52 + 1"
"n_fac": "2^52 * 3^3 * 5 * 13 + 1"
"nd": 7903817346035220479
"nd_hex": "0x6dafffffffffffff"
"nd_bit": "2^63 - 2^60 - 2^57 - 2^54 - 2^52 - 1"
"r2": 5062420639594976590
"r2_hex": "0x464154bff6aa154e"
"r2_bit": "2^62 + 2^59 - 2^57 + 2^54 + 2^48 + 2^46 + 2^44 + 2^42 + 2^40 - 2^38 - 2^27 - 2^25 + 2^23 + 2^21 + 2^19 + 2^17 + 2^12 + 2^10 + 2^8 + 2^6 + 2^4 - 2"
"znprimroot": 17
- "n": 6147413491360727041
"n_hex": "0x5550000000000001"
"n_bit": "2^62 + 2^60 + 2^58 + 2^56 + 2^54 + 2^52 + 1"
"n_fac": "2^52 * 3 * 5 * 7 * 13 + 1"
"nd": 6147413491360727039
"nd_hex": "0x554fffffffffffff"
"nd_bit": "2^62 + 2^60 + 2^58 + 2^56 + 2^54 + 2^52 - 1"
"r2": 4621818292753874935
"r2_hex": "0x4023ff3ff3ff3ff7"
"r2_bit": "2^62 + 2^53 + 2^50 - 2^40 + 2^38 - 2^28 + 2^26 - 2^16 + 2^14 - 2^3 - 1"
"znprimroot": 29
- "n": 3377699720527872001
"n_hex": "0x2ee0000000000001"
"n_bit": "2^62 - 2^60 - 2^56 - 2^53 + 1"
"n_fac": "2^53 * 3 * 5^3 + 1"
"nd": 3377699720527871999
"nd_hex": "0x2edfffffffffffff"
"nd_bit": "2^62 - 2^60 - 2^56 - 2^53 - 1"
"r2": 1988765576248798399
"r2_hex": "0x1b9983c131d5acbf"
"r2_bit": "2^61 - 2^58 - 2^55 + 2^53 - 2^51 + 2^49 - 2^47 + 2^42 - 2^38 + 2^32 + 2^30 - 2^28 + 2^25 - 2^21 - 2^19 - 2^17 - 2^14 - 2^12 - 2^10 + 2^8 - 2^6 - 1"
"znprimroot": 26
- "n": 9097271247288401921
"n_hex": "0x7e40000000000001"
"n_bit": "2^63 - 2^57 + 2^54 + 1"
"n_fac": "2^54 * 5 * 101 + 1"
"nd": 9097271247288401919
"nd_hex": "0x7e3fffffffffffff"
"nd_bit": "2^63 - 2^57 + 2^54 - 1"
"r2": 3817304552273617011
"r2_hex": "0x34f9ca43edc02073"
"r2_bit": "2^62 - 2^60 + 2^58 + 2^56 - 2^51 + 2^49 - 2^46 + 2^43 + 2^41 + 2^38 + 2^34 - 2^28 - 2^25 - 2^22 + 2^13 + 2^7 - 2^4 + 2^2 - 1"
"znprimroot": 6
- "n": 8592868089022906369
"n_hex": "0x7740000000000001"
"n_bit": "2^63 - 2^59 - 2^56 + 2^54 + 1"
"n_fac": "2^54 * 3^2 * 53 + 1"
"nd": 8592868089022906367
"nd_hex": "0x773fffffffffffff"
"nd_bit": "2^63 - 2^59 - 2^56 + 2^54 - 1"
"r2": 3898889881177989654
"r2_hex": "0x361ba3b091faa216"
"r2_bit": "2^62 - 2^59 - 2^57 + 2^53 - 2^50 - 2^47 + 2^45 + 2^42 - 2^38 - 2^36 + 2^31 + 2^28 + 2^25 - 2^19 + 2^17 + 2^15 + 2^13 + 2^9 + 2^5 - 2^3 - 2"
"znprimroot": 11
- "n": 7097673012735901697
"n_hex": "0x6280000000000001"
"n_bit": "2^63 - 2^61 + 2^57 + 2^55 + 1"
"n_fac": "2^55 * 197 + 1"
"nd": 7097673012735901695
"nd_hex": "0x627fffffffffffff"
"nd_bit": "2^63 - 2^61 + 2^57 + 2^55 - 1"
"r2": 6713243919670611035
"r2_hex": "0x5d2a3bc6d2848c5b"
"r2_bit": "2^63 - 2^61 - 2^58 + 2^56 + 2^53 + 2^51 + 2^49 + 2^46 - 2^42 - 2^38 + 2^35 - 2^32 - 2^30 + 2^28 + 2^25 + 2^23 + 2^18 + 2^15 + 2^12 - 2^10 + 2^7 - 2^5 - 2^2 - 1"
"znprimroot": 3
- "n": 6269010681299730433
"n_hex": "0x5700000000000001"
"n_bit": "2^63 - 2^61 - 2^59 - 2^56 + 1"
"n_fac": "2^56 * 3 * 29 + 1"
"nd": 6269010681299730431
"nd_hex": "0x56ffffffffffffff"
"nd_bit": "2^63 - 2^61 - 2^59 - 2^56 - 1"
"r2": 985615366725680966
"r2_hex": "0xdad9bf43ad9bf46"
"r2_bit": "2^60 - 2^57 - 2^54 - 2^52 - 2^49 - 2^47 + 2^45 - 2^42 - 2^36 + 2^34 + 2^30 - 2^26 - 2^24 - 2^21 - 2^19 + 2^17 - 2^14 - 2^8 + 2^6 + 2^3 - 2"
"znprimroot": 5
- "n": 1945555039024054273
"n_hex": "0x1b00000000000001"
"n_bit": "2^61 - 2^58 - 2^56 + 1"
"n_fac": "2^56 * 3^3 + 1"
"nd": 1945555039024054271
"nd_hex": "0x1affffffffffffff"
"nd_bit": "2^61 - 2^58 - 2^56 - 1"
"r2": 1526553473692399260
"r2_hex": "0x152f684bda12f69c"
"r2_bit": "2^60 + 2^58 + 2^56 + 2^54 - 2^52 - 2^47 - 2^45 + 2^43 + 2^38 + 2^36 - 2^34 - 2^29 - 2^27 + 2^25 + 2^20 + 2^18 - 2^16 - 2^11 - 2^9 + 2^7 + 2^5 - 2^2"
"znprimroot": 5
- "n": 4179340454199820289
"n_hex": "0x3a00000000000001"
"n_bit": "2^62 - 2^59 + 2^57 + 1"
"n_fac": "2^57 * 29 + 1"
"nd": 4179340454199820287
"nd_hex": "0x39ffffffffffffff"
"nd_bit": "2^62 - 2^59 + 2^57 - 1"
"r2": 2559286960657440491
"r2_hex": "0x238469ee58469eeb"
"r2_bit": "2^61 + 2^58 - 2^55 + 2^50 + 2^47 - 2^45 + 2^43 + 2^41 - 2^36 - 2^33 + 2^31 - 2^29 - 2^27 + 2^22 + 2^19 - 2^17 + 2^15 + 2^13 - 2^8 - 2^4 - 2^2 - 1"
"znprimroot": 3
Raw
result_prime_0064.yaml
- "r": 64
"primes":
- "n": 18446744073709551427
"n_hex": "0xffffffffffffff43"
"n_bit": "2^64 - 2^8 + 2^6 + 2^2 - 1"
"n_fac": "2 * 3 * 23 * 133672058505141677 + 1"
"nd": 11907422100489763477
"nd_hex": "0xa53fa94fea53fa95"
"nd_bit": "2^63 + 2^61 + 2^58 + 2^56 + 2^54 - 2^47 + 2^45 + 2^43 + 2^40 + 2^38 + 2^36 - 2^29 + 2^27 + 2^25 + 2^22 + 2^20 + 2^18 - 2^11 + 2^9 + 2^7 + 2^4 + 2^2 + 1"
"r2": 35721
"r2_hex": "0x8b89"
"r2_bit": "2^15 + 2^12 - 2^10 - 2^7 + 2^3 + 1"
"znprimroot": 2
- "n": 18446744073709550791
"n_hex": "0xfffffffffffffcc7"
"n_bit": "2^64 - 2^10 + 2^8 - 2^6 + 2^3 - 1"
"n_fac": "2 * 3^2 * 5 * 37 * 3727 * 1486332917869 + 1"
"nd": 10374896060849978121
"nd_hex": "0x8ffb08ffb08ffb09"
"nd_bit": "2^63 + 2^60 - 2^50 - 2^48 + 2^43 + 2^40 - 2^30 - 2^28 + 2^23 + 2^20 - 2^10 - 2^8 + 2^3 + 1"
"r2": 680625
"r2_hex": "0xa62b1"
"r2_bit": "2^19 + 2^17 + 2^15 - 2^13 + 2^10 - 2^8 - 2^6 - 2^4 + 1"
"znprimroot": 11
- "n": 18446744073709551557
"n_hex": "0xffffffffffffffc5"
"n_bit": "2^64 - 2^6 + 2^2 + 1"
"n_fac": "2^2 * 11 * 137 * 547 * 5594472617641 + 1"
"nd": 14694863923124558067
"nd_hex": "0xcbeea4e1a08ad8f3"
"nd_bit": "2^64 - 2^62 + 2^60 - 2^58 - 2^52 - 2^49 + 2^47 + 2^45 + 2^42 + 2^40 - 2^37 + 2^33 - 2^31 + 2^29 + 2^23 + 2^20 - 2^18 - 2^16 - 2^13 - 2^11 + 2^8 - 2^4 + 2^2 - 1"
"r2": 3481
"r2_hex": "0xd99"
"r2_bit": "2^12 - 2^9 - 2^7 + 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 18446744073709550773
"n_hex": "0xfffffffffffffcb5"
"n_bit": "2^64 - 2^10 + 2^8 - 2^6 - 2^4 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 512409557603043077 + 1"
"nd": 17046279517698387555
"nd_hex": "0xec908ce8026dee63"
"nd_bit": "2^64 - 2^60 - 2^58 + 2^55 + 2^52 + 2^47 + 2^44 - 2^42 + 2^40 - 2^37 + 2^35 + 2^25 + 2^23 - 2^20 - 2^17 - 2^12 - 2^9 + 2^7 - 2^5 + 2^2 - 1"
"r2": 710649
"r2_hex": "0xad7f9"
"r2_bit": "2^20 - 2^18 - 2^16 - 2^13 - 2^11 - 2^3 + 1"
"znprimroot": 2
- "n": 18446744073709550341
"n_hex": "0xfffffffffffffb05"
"n_bit": "2^64 - 2^10 - 2^8 + 2^2 + 1"
"n_fac": "2^2 * 3^2 * 5 * 7^2 * 17 * 1381 * 89085810881 + 1"
"nd": 11053578409658115635
"nd_hex": "0x996632ffcc996633"
"nd_bit": "2^63 + 2^61 - 2^59 + 2^57 - 2^55 - 2^53 + 2^51 - 2^49 + 2^46 - 2^44 + 2^42 - 2^40 - 2^30 + 2^28 - 2^26 + 2^23 + 2^21 - 2^19 + 2^17 - 2^15 - 2^13 + 2^11 - 2^9 + 2^6 - 2^4 + 2^2 - 1"
"r2": 1625625
"r2_hex": "0x18ce19"
"r2_bit": "2^21 - 2^19 + 2^16 - 2^14 + 2^12 - 2^9 + 2^5 - 2^3 + 1"
"znprimroot": 2
- "n": 18446744073709551337
"n_hex": "0xfffffffffffffee9"
"n_bit": "2^64 - 2^8 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 3 * 11 * 53 * 211 * 863 * 7240135181 + 1"
"nd": 8066318197105968807
"nd_hex": "0x6ff151a9bfc546a7"
"nd_bit": "2^63 - 2^60 - 2^52 + 2^48 + 2^46 + 2^44 + 2^41 - 2^39 + 2^37 + 2^35 + 2^33 - 2^30 - 2^22 + 2^18 + 2^16 + 2^14 + 2^11 - 2^9 + 2^7 + 2^5 + 2^3 - 1"
"r2": 77841
"r2_hex": "0x13011"
"r2_bit": "2^16 + 2^14 - 2^12 + 2^4 + 1"
"znprimroot": 5
- "n": 18446744073709551521
"n_hex": "0xffffffffffffffa1"
"n_bit": "2^64 - 2^7 + 2^5 + 1"
"n_fac": "2^5 * 5 * 2663 * 43294085790719 + 1"
"nd": 5631111348816599967
"nd_hex": "0x4e25b9efd4e25b9f"
"nd_bit": "2^62 + 2^60 - 2^57 + 2^53 + 2^51 - 2^49 - 2^46 - 2^43 + 2^41 - 2^36 - 2^30 + 2^28 + 2^26 + 2^24 - 2^21 + 2^17 + 2^15 - 2^13 - 2^10 - 2^7 + 2^5 - 1"
"r2": 9025
"r2_hex": "0x2341"
"r2_bit": "2^13 + 2^10 - 2^8 + 2^6 + 1"
"znprimroot": 3
- "n": 18446744073709546561
"n_hex": "0xffffffffffffec41"
"n_bit": "2^64 - 2^12 - 2^10 + 2^6 + 1"
"n_fac": "2^6 * 3^2 * 5 * 7 * 915017067148291c + 1"
"nd": 10451330371336133695
"nd_hex": "0x910a959965bddc3f"
"nd_bit": "2^63 + 2^60 + 2^56 + 2^51 + 2^49 + 2^47 + 2^45 - 2^43 - 2^41 - 2^39 + 2^37 - 2^35 + 2^33 - 2^31 - 2^29 + 2^27 - 2^25 - 2^22 - 2^17 - 2^13 - 2^10 + 2^6 - 1"
"r2": 25553025
"r2_hex": "0x185e881"
"r2_bit": "2^25 - 2^23 + 2^19 - 2^17 - 2^13 + 2^11 + 2^7 + 1"
"znprimroot": 13
- "n": 18446744073709549441
"n_hex": "0xfffffffffffff781"
"n_bit": "2^64 - 2^11 - 2^7 + 1"
"n_fac": "2^7 * 3^2 * 5 * 163 * 19647605736313c + 1"
"nd": 12840630127630464895
"nd_hex": "0xb23315118997b77f"
"nd_bit": "2^64 - 2^62 - 2^60 + 2^57 + 2^54 - 2^52 + 2^50 - 2^48 + 2^44 + 2^42 + 2^40 + 2^36 + 2^33 - 2^31 + 2^27 + 2^25 - 2^23 + 2^21 - 2^19 - 2^14 - 2^11 - 2^7 - 1"
"r2": 4730625
"r2_hex": "0x482f01"
"r2_bit": "2^22 + 2^19 + 2^14 - 2^12 - 2^8 + 1"
"znprimroot": 11
- "n": 18446744073709472641
"n_hex": "0xfffffffffffecb81"
"n_bit": "2^64 - 2^16 - 2^14 + 2^12 - 2^10 - 2^7 + 1"
"n_fac": "2^7 * 3 * 5 * 7 * 1372525600722431 + 1"
"nd": 11828106022774016895
"nd_hex": "0xa425dfc27d1a8b7f"
"nd_bit": "2^63 + 2^61 + 2^58 + 2^53 + 2^51 - 2^49 - 2^45 - 2^38 + 2^33 + 2^31 - 2^26 + 2^24 + 2^21 - 2^19 + 2^17 + 2^15 + 2^12 - 2^10 - 2^7 - 1"
"r2": 6237050625
"r2_hex": "0x173c1d701"
"r2_bit": "2^33 - 2^31 - 2^28 + 2^26 - 2^22 + 2^17 - 2^13 - 2^11 - 2^8 + 1"
"znprimroot": 11
- "n": 18446744073708115201
"n_hex": "0xffffffffffea1501"
"n_bit": "2^64 - 2^21 + 2^19 + 2^17 + 2^12 + 2^10 + 2^8 + 1"
"n_fac": "2^8 * 3^2 * 5^2 * 7 * 17 * 167 * 16115129749 + 1"
"nd": 15135945103588267263
"nd_hex": "0xd20dade0c73114ff"
"nd_bit": "2^64 - 2^62 + 2^60 + 2^57 + 2^52 - 2^49 - 2^46 - 2^44 - 2^41 - 2^37 + 2^32 - 2^30 + 2^27 - 2^24 + 2^22 - 2^20 + 2^16 + 2^12 + 2^10 + 2^8 - 1"
"r2": 2063288052225
"r2_hex": "0x1e0658d2a01"
"r2_bit": "2^41 - 2^37 + 2^31 - 2^29 + 2^27 - 2^25 - 2^23 + 2^20 - 2^18 + 2^16 + 2^13 + 2^11 + 2^9 + 1"
"znprimroot": 19
- "n": 18446744073709432321
"n_hex": "0xfffffffffffe2e01"
"n_bit": "2^64 - 2^17 + 2^14 - 2^12 - 2^9 + 1"
"n_fac": "2^9 * 3 * 5 * 7 * 613 * 559757585939c + 1"
"nd": 10022274784302870015
"nd_hex": "0x8b1645d0e7ba2dff"
"nd_bit": "2^63 + 2^60 - 2^58 - 2^56 + 2^53 - 2^51 - 2^49 + 2^46 + 2^43 - 2^41 - 2^38 + 2^36 + 2^32 - 2^29 + 2^27 - 2^22 - 2^19 + 2^17 + 2^14 - 2^12 - 2^9 - 1"
"r2": 14231297025
"r2_hex": "0x350405c01"
"r2_bit": "2^34 - 2^32 + 2^30 + 2^28 + 2^22 + 2^15 - 2^13 - 2^10 + 1"
"znprimroot": 17
- "n": 18446744073709186561
"n_hex": "0xfffffffffffa6e01"
"n_bit": "2^64 - 2^19 + 2^17 + 2^15 - 2^12 - 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5 * 13 * 89 * 691996485527c + 1"
"nd": 2511107915242696191
"nd_hex": "0x22d93f5830b66dff"
"nd_bit": "2^61 + 2^58 - 2^56 - 2^53 - 2^51 + 2^48 + 2^46 - 2^39 - 2^37 - 2^35 + 2^30 - 2^28 + 2^24 - 2^22 - 2^19 - 2^17 + 2^15 - 2^12 - 2^9 - 1"
"r2": 133265153025
"r2_hex": "0x1f0738dc01"
"r2_bit": "2^37 - 2^32 + 2^27 - 2^24 + 2^22 - 2^19 + 2^16 - 2^13 - 2^10 + 1"
"znprimroot": 11
- "n": 18446744073709550593
"n_hex": "0xfffffffffffffc01"
"n_bit": "2^64 - 2^10 + 1"
"n_fac": "2^10 * 3^4 * 7 * 19 * 73 * 22906579627c + 1"
"nd": 17292695568609442815
"nd_hex": "0xeffbfeffbfeffbff"
"nd_bit": "2^64 - 2^60 - 2^50 - 2^40 - 2^30 - 2^20 - 2^10 - 1"
"r2": 1046529
"r2_hex": "0xff801"
"r2_bit": "2^20 - 2^11 + 1"
"znprimroot": 5
- "n": 18446744073709271041
"n_hex": "0xfffffffffffbb801"
"n_bit": "2^64 - 2^18 - 2^14 - 2^11 + 1"
"n_fac": "2^11 * 3 * 5 * 7^2 * 83^2 * 4021 * 442397 + 1"
"nd": 8536422716872046591
"nd_hex": "0x7677773babbbb7ff"
"nd_bit": "2^63 - 2^59 - 2^57 + 2^55 - 2^51 - 2^47 - 2^43 - 2^40 + 2^38 - 2^34 - 2^30 - 2^28 - 2^26 - 2^22 - 2^18 - 2^14 - 2^11 - 1"
"r2": 78722330625
"r2_hex": "0x1254377001"
"r2_bit": "2^36 + 2^33 + 2^30 + 2^28 + 2^26 + 2^22 - 2^19 - 2^15 - 2^12 + 1"
"znprimroot": 11
- "n": 18446744073709547521
"n_hex": "0xfffffffffffff001"
"n_bit": "2^64 - 2^12 + 1"
"n_fac": "2^12 * 3 * 5 * 53 * 157 * 1613 * 2731 * 8191 + 1"
"nd": 17293541025389735935
"nd_hex": "0xeffeffeffeffefff"
"nd_bit": "2^64 - 2^60 - 2^48 - 2^36 - 2^24 - 2^12 - 1"
"r2": 16769025
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"r2_bit": "2^24 - 2^13 + 1"
"znprimroot": 17
- "n": 18446744073709264897
"n_hex": "0xfffffffffffba001"
"n_bit": "2^64 - 2^18 - 2^15 + 2^13 + 1"
"n_fac": "2^13 * 3^2 * 11 * 22745452663487c + 1"
"nd": 11717313365825789951
"nd_hex": "0xa29c426cdbfb9fff"
"nd_bit": "2^63 + 2^61 + 2^57 + 2^55 + 2^53 - 2^50 + 2^46 + 2^41 + 2^39 - 2^36 - 2^34 + 2^32 - 2^29 - 2^26 - 2^18 - 2^15 + 2^13 - 1"
"r2": 82207784961
"r2_hex": "0x1323f74001"
"r2_bit": "2^36 + 2^34 - 2^32 + 2^29 + 2^26 - 2^19 - 2^16 + 2^14 + 1"
"znprimroot": 15
- "n": 18446744073708625921
"n_hex": "0xfffffffffff1e001"
"n_bit": "2^64 - 2^20 + 2^17 - 2^13 + 1"
"n_fac": "2^13 * 3 * 5 * 7 * 293 * 73193558059 + 1"
"nd": 8713856941873553407
"nd_hex": "0x78edd6b87bf1dfff"
"nd_bit": "2^63 - 2^59 + 2^56 - 2^52 - 2^49 - 2^45 - 2^43 - 2^40 - 2^38 - 2^35 + 2^31 - 2^26 - 2^20 + 2^17 - 2^13 - 1"
"r2": 856911233025
"r2_hex": "0xc783e3c001"
"r2_bit": "2^40 - 2^38 + 2^35 - 2^31 + 2^26 - 2^21 + 2^18 - 2^14 + 1"
"znprimroot": 19
- "n": 18446744073706905601
"n_hex": "0xffffffffffd7a001"
"n_bit": "2^64 - 2^21 - 2^19 - 2^15 + 2^13 + 1"
"n_fac": "2^13 * 3^2 * 5^2 * 7 * 227 * 6298300297 + 1"
"nd": 9932420842750713855
"nd_hex": "0x89d70c21dbd79fff"
"nd_bit": "2^63 + 2^59 + 2^57 - 2^53 - 2^51 - 2^48 + 2^44 - 2^42 + 2^37 + 2^33 - 2^29 - 2^26 - 2^21 - 2^19 - 2^15 + 2^13 - 1"
"r2": 7001395380225
"r2_hex": "0x65e23af4001"
"r2_bit": "2^43 - 2^41 + 2^39 - 2^37 - 2^33 + 2^29 + 2^26 - 2^22 - 2^20 - 2^16 + 2^14 + 1"
"znprimroot": 11
- "n": 18446744073709436929
"n_hex": "0xfffffffffffe4001"
"n_bit": "2^64 - 2^17 + 2^14 + 1"
"n_fac": "2^14 * 3 * 139 * 317 * 8517349453 + 1"
"nd": 11455648908923781119
"nd_hex": "0x9efaa3fceffe3fff"
"nd_bit": "2^63 + 2^61 - 2^56 - 2^51 + 2^49 + 2^47 + 2^45 + 2^42 - 2^34 + 2^32 - 2^28 - 2^17 + 2^14 - 1"
"r2": 13153107969
"r2_hex": "0x30ffc8001"
"r2_bit": "2^34 - 2^32 + 2^28 - 2^18 + 2^15 + 1"
"znprimroot": 7
- "n": 18446744073708748801
"n_hex": "0xfffffffffff3c001"
"n_bit": "2^64 - 2^20 + 2^18 - 2^14 + 1"
"n_fac": "2^14 * 3^3 * 5^2 * 1667999861989c + 1"
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"r2_bit": "2^63 - 2^60 + 2^58 - 2^53 + 2^51 - 2^43 + 2^41 - 2^38 - 2^32 + 2^27 - 2^25 - 2^21 - 2^19 + 2^16 - 2^13 + 2^11 + 2^9 - 2^5 + 2^3 - 2"
"znprimroot": 7
- "n": 15841411689275719681
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"nd": 15841411689275719679
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"nd_bit": "2^64 - 2^61 - 2^58 - 2^53 - 2^51 - 1"
"r2": 5309104110232351131
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"r2_bit": "2^62 + 2^59 + 2^57 - 2^54 - 2^52 - 2^49 - 2^46 - 2^43 + 2^41 + 2^36 - 2^32 + 2^30 - 2^27 - 2^25 - 2^19 - 2^16 + 2^14 - 2^12 + 2^9 - 2^7 + 2^5 - 2^2 - 1"
"znprimroot": 37
- "n": 14085007834601226241
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"n_bit": "2^64 - 2^62 + 2^58 - 2^55 - 2^51 + 1"
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"nd": 14085007834601226239
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"r2": 11885370576600029033
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"r2_bit": "2^63 + 2^61 + 2^58 + 2^56 - 2^52 + 2^48 + 2^46 + 2^44 + 2^41 - 2^39 + 2^36 + 2^33 - 2^31 - 2^29 + 2^27 + 2^25 + 2^21 - 2^13 - 2^11 - 2^7 - 2^5 + 2^3 + 1"
"znprimroot": 7
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"nd": 13477021884906209279
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"nd_bit": "2^64 - 2^62 - 2^58 - 2^56 + 2^51 - 1"
"r2": 1777024095374382114
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"r2_bit": "2^61 - 2^59 + 2^55 + 2^53 + 2^51 + 2^48 + 2^46 + 2^41 - 2^29 + 2^27 + 2^25 + 2^21 - 2^19 + 2^17 - 2^15 + 2^12 + 2^10 + 2^5 + 2"
"znprimroot": 13
- "n": 18433233274827440129
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"nd": 18433233274827440127
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"nd_bit": "2^64 - 2^54 + 2^52 - 1"
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"r2_bit": "2^64 - 2^61 - 2^59 + 2^56 - 2^43 - 2^40 - 2^33 + 2^30 + 2^28 - 2^22 - 2^20 - 2^16 - 2^12 + 2^8 - 2^6 + 2^4 - 1"
"znprimroot": 3
- "n": 18307132485261066241
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"n_bit": "2^64 - 2^57 + 2^52 + 1"
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"nd": 18307132485261066239
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"r2": 7425371096913553552
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"r2_bit": "2^63 - 2^61 + 2^59 - 2^56 + 2^52 - 2^50 + 2^46 - 2^43 - 2^38 - 2^36 - 2^34 - 2^29 - 2^26 + 2^24 - 2^18 + 2^13 + 2^11 + 2^7 + 2^4"
"znprimroot": 19
- "n": 14659216787090964481
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"n_bit": "2^64 - 2^62 + 2^60 - 2^58 - 2^55 - 2^52 + 1"
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"nd": 14659216787090964479
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"r2": 8069141651987562478
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"r2_bit": "2^63 - 2^60 - 2^50 - 2^47 - 2^45 - 2^43 + 2^41 - 2^39 + 2^36 + 2^34 + 2^31 + 2^28 + 2^24 + 2^19 - 2^16 - 2^4 - 2"
"znprimroot": 19
- "n": 18023405708736724993
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"r2_bit": "2^61 + 2^58 - 2^56 - 2^53 - 2^50 + 2^48 - 2^46 - 2^44 - 2^42 + 2^39 - 2^36 + 2^34 + 2^32 + 2^30 - 2^28 + 2^23 - 2^18 + 2^16 - 2^13 - 2^9 - 2^7 + 2^5 - 2^3 - 1"
"znprimroot": 5
- "n": 17915319317679833089
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"nd": 17915319317679833087
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"r2_bit": "2^64 - 2^61 + 2^59 + 2^57 + 2^55 + 2^53 + 2^51 - 2^40 - 2^35 + 2^31 - 2^29 + 2^27 - 2^16 - 2^11 + 2^7 - 2^5 + 2^3 + 2"
"znprimroot": 7
- "n": 15267202736785981441
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"r2": 13046787299973005005
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"r2_bit": "2^64 - 2^62 - 2^60 + 2^58 + 2^56 + 2^52 - 2^47 - 2^36 - 2^34 + 2^32 - 2^30 - 2^28 - 2^26 - 2^24 - 2^19 - 2^8 - 2^6 + 2^4 - 2^2 + 1"
"znprimroot": 7
- "n": 9322451228656926721
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"r2_bit": "2^61 - 2^59 - 2^56 + 2^54 - 2^52 + 2^48 + 2^43 + 2^40 + 2^37 + 2^35 - 2^32 - 2^30 + 2^28 + 2^26 + 2^24 + 2^22 - 2^19 - 2^17 - 2^14 - 2^12 - 2^10 + 2^7 - 2^5 + 2^3 + 2"
"znprimroot": 29
- "n": 12700150949184798721
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"nd": 12700150949184798719
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"r2_bit": "2^55 - 2^53 + 2^51 + 2^49 + 2^45 - 2^40 + 2^38 - 2^35 + 2^33 + 2^31 - 2^27 - 2^25 + 2^23 - 2^21 + 2^15 + 2^13 - 2^11 - 2^8 + 2^4 + 1"
"znprimroot": 7
- "n": 17798225727368200193
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"nd": 17798225727368200191
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"r2_bit": "2^64 - 2^61 + 2^59 - 2^57 - 2^54 - 2^52 - 2^50 + 2^44 - 2^42 + 2^39 - 2^36 - 2^28 - 2^23 - 2^20 - 2^18 - 2^16 - 2^14 + 2^8 - 2^6 + 2^3 + 1"
"znprimroot": 3
- "n": 17726168133330272257
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"r2": 10058771460416444401
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"r2_bit": "2^63 + 2^60 - 2^58 - 2^55 + 2^53 - 2^51 - 2^44 - 2^39 - 2^37 - 2^35 + 2^33 - 2^31 - 2^24 - 2^19 - 2^17 - 2^15 + 2^13 - 2^11 - 2^4 + 1"
"znprimroot": 7
- "n": 10808639105689190401
"n_hex": "0x9600000000000001"
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"nd": 10808639105689190399
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"r2": 4258123423681288168
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"r2_bit": "2^62 - 2^58 - 2^56 + 2^53 - 2^51 - 2^45 + 2^42 + 2^40 - 2^38 - 2^36 + 2^33 - 2^31 - 2^25 + 2^22 + 2^20 - 2^18 - 2^16 + 2^13 - 2^11 - 2^5 + 2^3"
"znprimroot": 7
- "n": 15564440312192434177
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"r2": 3501465310287461188
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"r2_bit": "2^62 - 2^60 + 2^55 + 2^53 - 2^51 - 2^46 - 2^44 + 2^42 + 2^37 + 2^35 - 2^33 - 2^28 - 2^26 + 2^24 + 2^19 + 2^17 - 2^15 - 2^10 - 2^8 + 2^6 + 2^2"
"znprimroot": 5
Raw
result_prime_0094.yaml
This file has been truncated, but you can view the full file.
- "r": 94
"primes":
- "n": 19807040628566084398385987479
"n_hex": "0x3fffffffffffffffffffff97"
"n_bit": "2^94 - 2^7 + 2^5 - 2^3 - 1"
"n_fac": "2 * 3^2 * 61 * 18039199115269657922027311c + 1"
"nd": 19052486699858804992733188057
"nd_hex": "0x3d8fd8fd8fd8fd8fd8fd8fd9"
"nd_bit": "2^94 - 2^89 - 2^87 + 2^84 - 2^77 - 2^75 + 2^72 - 2^65 - 2^63 + 2^60 - 2^53 - 2^51 + 2^48 - 2^41 - 2^39 + 2^36 - 2^29 - 2^27 + 2^24 - 2^17 - 2^15 + 2^12 - 2^5 - 2^3 + 1"
"r2": 11025
"r2_hex": "0x2b11"
"r2_bit": "2^14 - 2^12 - 2^10 - 2^8 + 2^4 + 1"
"znprimroot": 7
- "n": 19807040628566084398385985931
"n_hex": "0x3ffffffffffffffffffff98b"
"n_bit": "2^94 - 2^11 + 2^9 - 2^7 + 2^4 - 2^2 - 1"
"n_fac": "2 * 3^2 * 5 * 7 * 457 * 6689 * 10284937264148682407c + 1"
"nd": 11311461798769742088370461149
"nd_hex": "0x248c9f34cf8694fc20d519dd"
"nd_bit": "2^93 + 2^90 + 2^87 + 2^84 - 2^82 + 2^79 + 2^77 - 2^72 + 2^70 - 2^68 + 2^66 + 2^64 - 2^62 + 2^60 - 2^55 + 2^51 - 2^49 + 2^47 + 2^44 + 2^42 + 2^40 - 2^34 + 2^29 + 2^24 - 2^22 + 2^20 + 2^18 + 2^16 + 2^13 - 2^11 + 2^9 - 2^5 - 2^2 + 1"
"r2": 2732409
"r2_hex": "0x29b179"
"r2_bit": "2^21 + 2^19 + 2^17 - 2^14 - 2^12 + 2^9 - 2^7 - 2^3 + 1"
"znprimroot": 2
- "n": 19807040628566084398385987581
"n_hex": "0x3ffffffffffffffffffffffd"
"n_bit": "2^94 - 2^2 + 1"
"n_fac": "2^2 * 3 * 5 * 47 * 277 * 1013 * 1657 * 15106322819245967c + 1"
"nd": 13204693752377389598923991723
"nd_hex": "0x2aaaaaaaaaaaaaaaaaaaaaab"
"nd_bit": "2^94 - 2^92 - 2^90 - 2^88 - 2^86 - 2^84 - 2^82 - 2^80 - 2^78 - 2^76 - 2^74 - 2^72 - 2^70 - 2^68 - 2^66 - 2^64 - 2^62 - 2^60 - 2^58 - 2^56 - 2^54 - 2^52 - 2^50 - 2^48 - 2^46 - 2^44 - 2^42 - 2^40 - 2^38 - 2^36 - 2^34 - 2^32 - 2^30 - 2^28 - 2^26 - 2^24 - 2^22 - 2^20 - 2^18 - 2^16 - 2^14 - 2^12 - 2^10 - 2^8 - 2^6 - 2^4 - 2^2 - 1"
"r2": 9
"r2_hex": "0x9"
"r2_bit": "2^3 + 1"
"znprimroot": 10
- "n": 19807040628566084398385985301
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"n_bit": "2^94 - 2^11 - 2^8 + 2^4 + 2^2 + 1"
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"nd": 5925628011086568394260897731
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"r2": 5212089
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"znprimroot": 10
- "n": 19807040628566084398385987177
"n_hex": "0x3ffffffffffffffffffffe69"
"n_bit": "2^94 - 2^9 + 2^7 - 2^5 + 2^3 + 1"
"n_fac": "2^3 * 7 * 3947 * 89611642787316245604193c + 1"
"nd": 12945142032428939680517623335
"nd_hex": "0x29d3f873bc119c9e81928e27"
"nd_bit": "2^93 + 2^91 + 2^89 - 2^86 + 2^84 + 2^82 - 2^75 + 2^71 - 2^68 + 2^66 - 2^62 - 2^58 + 2^52 + 2^49 - 2^47 + 2^45 - 2^42 + 2^39 + 2^37 - 2^33 + 2^31 + 2^25 - 2^23 + 2^20 + 2^17 + 2^15 + 2^12 - 2^9 + 2^5 + 2^3 - 1"
"r2": 165649
"r2_hex": "0x28711"
"r2_bit": "2^17 + 2^15 + 2^11 - 2^8 + 2^4 + 1"
"znprimroot": 3
- "n": 19807040628566084398385987153
"n_hex": "0x3ffffffffffffffffffffe51"
"n_bit": "2^94 - 2^9 + 2^6 + 2^4 + 1"
"n_fac": "2^4 * 23 * 53823479968929577169527139c + 1"
"nd": 6112149428304615371195675983
"nd_hex": "0x13bfd9fc6faa77fb3f8df54f"
"nd_bit": "2^92 + 2^90 - 2^86 - 2^77 - 2^75 + 2^73 - 2^66 + 2^63 - 2^60 - 2^55 + 2^53 + 2^51 + 2^49 + 2^47 - 2^43 - 2^34 - 2^32 + 2^30 - 2^23 + 2^20 - 2^17 - 2^12 + 2^10 + 2^8 + 2^6 + 2^4 - 1"
"r2": 185761
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"znprimroot": 3
- "n": 19807040628566084398385986801
"n_hex": "0x3ffffffffffffffffffffcf1"
"n_bit": "2^94 - 2^10 + 2^8 - 2^4 + 1"
"n_fac": "2^4 * 3 * 5^2 * 137 * 120480782412202459844197c + 1"
"nd": 6273494349788491610216762351
"nd_hex": "0x1445501a27e33a860c6c8bef"
"nd_bit": "2^92 + 2^90 + 2^86 + 2^82 + 2^80 + 2^78 + 2^76 + 2^69 - 2^67 + 2^65 + 2^61 + 2^59 - 2^53 + 2^50 - 2^48 + 2^46 - 2^43 + 2^41 + 2^39 + 2^35 - 2^33 + 2^28 - 2^26 + 2^23 - 2^20 - 2^18 + 2^15 + 2^12 - 2^10 - 2^4 - 1"
"r2": 613089
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"znprimroot": 7
- "n": 19807040628566084398385981521
"n_hex": "0x3fffffffffffffffffffe851"
"n_bit": "2^94 - 2^13 + 2^11 + 2^6 + 2^4 + 1"
"n_fac": "2^4 * 3^4 * 5 * 7 * 5477 * 79726703156305092091c + 1"
"nd": 13011948346293701823976808271
"nd_hex": "0x2a0b3b3d441b311b10ad9f4f"
"nd_bit": "2^93 + 2^91 + 2^89 + 2^84 - 2^82 - 2^80 + 2^78 - 2^74 - 2^72 + 2^70 - 2^66 + 2^64 + 2^62 + 2^58 + 2^53 - 2^50 - 2^48 + 2^46 - 2^44 + 2^40 + 2^37 - 2^34 - 2^32 + 2^28 + 2^24 - 2^22 - 2^20 - 2^17 - 2^15 + 2^13 - 2^8 + 2^6 + 2^4 - 1"
"r2": 36759969
"r2_hex": "0x230e9a1"
"r2_bit": "2^25 + 2^22 - 2^20 + 2^16 - 2^13 + 2^11 + 2^9 - 2^7 + 2^5 + 1"
"znprimroot": 39
- "n": 19807040628566084398385985697
"n_hex": "0x3ffffffffffffffffffff8a1"
"n_bit": "2^94 - 2^11 + 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 68774446626965570827729117c + 1"
"nd": 7452569605872771554241680543
"nd_hex": "0x18149effdd450db3c198149f"
"nd_bit": "2^93 - 2^91 + 2^84 + 2^82 + 2^79 + 2^77 - 2^72 - 2^61 - 2^58 + 2^56 + 2^54 + 2^50 + 2^48 + 2^44 - 2^41 - 2^38 - 2^36 + 2^34 - 2^30 + 2^25 - 2^23 + 2^21 - 2^19 + 2^12 + 2^10 + 2^7 + 2^5 - 1"
"r2": 3560769
"r2_hex": "0x365541"
"r2_bit": "2^22 - 2^19 - 2^17 + 2^14 + 2^12 + 2^10 + 2^8 + 2^6 + 1"
"znprimroot": 5
- "n": 19807040628566084398385969761
"n_hex": "0x3fffffffffffffffffffba61"
"n_bit": "2^94 - 2^14 - 2^11 + 2^9 + 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3 * 5 * 7 * 97 * 1277 * 47590216826047036439 + 1"
"nd": 3289504587362150581788841567
"nd_hex": "0xaa103b1003e8281a505965f"
"nd_bit": "2^91 + 2^89 + 2^87 + 2^85 + 2^80 + 2^74 - 2^70 - 2^68 + 2^64 + 2^54 - 2^49 + 2^47 + 2^41 + 2^39 + 2^33 - 2^31 + 2^29 + 2^26 + 2^24 + 2^19 - 2^17 - 2^15 + 2^13 - 2^11 - 2^9 + 2^7 - 2^5 - 1"
"r2": 317659329
"r2_hex": "0x12ef18c1"
"r2_bit": "2^28 + 2^26 - 2^24 - 2^20 - 2^16 + 2^13 - 2^11 + 2^8 - 2^6 + 1"
"znprimroot": 33
- "n": 19807040628566084398385939041
"n_hex": "0x3fffffffffffffffffff4261"
"n_bit": "2^94 - 2^16 + 2^14 + 2^9 + 2^7 - 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 13754889325393114165545791c + 1"
"nd": 11217175574643310594648645215
"nd_hex": "0x243ea1525be628b3c4df1e5f"
"nd_bit": "2^93 + 2^90 + 2^86 - 2^81 + 2^79 + 2^77 + 2^72 + 2^70 + 2^68 + 2^65 + 2^63 - 2^61 - 2^58 - 2^53 + 2^51 - 2^49 + 2^45 + 2^43 + 2^40 - 2^38 - 2^36 + 2^34 - 2^30 + 2^26 + 2^24 - 2^21 - 2^16 + 2^13 - 2^9 + 2^7 - 2^5 - 1"
"r2": 2356422849
"r2_hex": "0x8c7428c1"
"r2_bit": "2^31 + 2^28 - 2^26 + 2^23 - 2^20 + 2^18 + 2^13 + 2^11 + 2^8 - 2^6 + 1"
"znprimroot": 17
- "n": 19807040628566084398385895841
"n_hex": "0x3ffffffffffffffffffe99a1"
"n_bit": "2^94 - 2^17 + 2^15 + 2^13 - 2^11 + 2^9 - 2^7 + 2^5 + 1"
"n_fac": "2^5 * 3^2 * 5 * 7 * 37 * 83 * 227 * 293 * 607 * 3461 * 4579261829 + 1"
"nd": 1804251425535754960240145823
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"znprimroot": 26
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"nd": 18340327937529793222877209151
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"nd_bit": "2^94 - 2^90 - 2^88 + 2^86 + 2^82 - 2^80 - 2^78 + 2^74 - 2^71 + 2^65 - 2^62 - 2^60 + 2^58 - 2^56 - 2^54 + 2^50 + 2^48 + 2^44 + 2^42 - 2^40 + 2^38 + 2^36 + 2^33 + 2^30 + 2^27 - 2^25 - 2^23 - 2^21 + 2^19 - 2^17 - 2^15 - 2^13 + 2^9 + 2^6 - 1"
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"r2": 5303809
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"nd": 13963084395976400933758076671
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"r2": 959450625
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- "n": 19807040628566084398385944321
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"nd": 9957315179961717162020591359
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"nd_bit": "2^93 + 2^86 - 2^84 - 2^82 + 2^79 - 2^71 + 2^65 - 2^63 + 2^58 - 2^56 + 2^51 + 2^49 - 2^45 - 2^42 + 2^40 + 2^38 - 2^35 - 2^29 - 2^27 - 2^23 - 2^20 - 2^17 + 2^15 - 2^13 - 2^11 - 2^8 - 1"
"r2": 1871687169
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"znprimroot": 7
- "n": 19807040628566084398385970689
"n_hex": "0x3fffffffffffffffffffbe01"
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"n_fac": "2^9 * 38685626227668133590597599c + 1"
"nd": 12099938817841406160150445567
"nd_hex": "0x2718d5b5a98a538ce6fbbdff"
"nd_bit": "2^93 + 2^91 - 2^88 + 2^85 - 2^83 + 2^80 - 2^77 - 2^75 - 2^73 - 2^70 - 2^67 - 2^65 - 2^63 + 2^61 + 2^59 + 2^57 - 2^55 + 2^51 + 2^49 + 2^46 + 2^44 + 2^42 - 2^39 + 2^36 - 2^34 + 2^32 - 2^29 + 2^27 - 2^24 - 2^18 - 2^14 - 2^9 - 1"
"r2": 285441025
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"znprimroot": 3
- "n": 19807040628566084398385932801
"n_hex": "0x3fffffffffffffffffff2a01"
"n_bit": "2^94 - 2^16 + 2^13 + 2^11 + 2^9 + 1"
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"nd": 12458083692724048885880400383
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"r2": 3001177089
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"r2_bit": "2^32 - 2^30 - 2^28 + 2^26 - 2^24 - 2^21 + 2^17 + 2^14 + 2^12 + 2^10 + 1"
"znprimroot": 22
- "n": 19807040628566084398385687041
"n_hex": "0x3ffffffffffffffffffb6a01"
"n_bit": "2^94 - 2^18 - 2^15 - 2^13 + 2^11 + 2^9 + 1"
"n_fac": "2^9 * 3^2 * 5 * 13 * 66129275602851510411277c + 1"
"nd": 14852496019726946262073174527
"nd_hex": "0x2ffdb25e922deaab601769ff"
"nd_bit": "2^94 - 2^92 - 2^81 - 2^78 - 2^76 + 2^73 + 2^71 - 2^69 - 2^65 + 2^63 + 2^60 + 2^57 + 2^54 - 2^52 - 2^49 - 2^44 - 2^42 - 2^40 - 2^38 - 2^36 - 2^34 - 2^31 - 2^29 + 2^21 - 2^19 - 2^15 - 2^13 + 2^11 + 2^9 - 1"
"r2": 90326094849
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"r2_bit": "2^36 + 2^34 + 2^32 + 2^27 - 2^21 - 2^18 - 2^16 - 2^14 + 2^12 + 2^10 + 1"
"znprimroot": 53
- "n": 19807040628566084398385851393
"n_hex": "0x3ffffffffffffffffffdec01"
"n_bit": "2^94 - 2^17 - 2^12 - 2^10 + 1"
"n_fac": "2^10 * 3 * 6447604371278022265099561c + 1"
"nd": 11014867620369257396454681599
"nd_hex": "0x239748f22ea6957c6e6debff"
"nd_bit": "2^93 + 2^90 - 2^87 + 2^85 - 2^83 - 2^80 + 2^78 + 2^75 + 2^72 - 2^68 + 2^65 + 2^62 - 2^60 - 2^57 + 2^55 + 2^53 + 2^51 - 2^49 + 2^47 + 2^45 - 2^43 - 2^41 - 2^39 - 2^34 + 2^31 - 2^28 - 2^25 + 2^23 - 2^20 - 2^17 - 2^12 - 2^10 - 1"
"r2": 18547988481
"r2_hex": "0x4518bd801"
"r2_bit": "2^34 + 2^30 + 2^28 + 2^25 - 2^23 + 2^20 - 2^18 - 2^13 - 2^11 + 1"
"znprimroot": 5
- "n": 19807040628566084398385648641
"n_hex": "0x3ffffffffffffffffffad401"
"n_bit": "2^94 - 2^18 - 2^16 - 2^14 + 2^12 + 2^10 + 1"
"n_fac": "2^10 * 3 * 5 * 353 * 3653033638117859640283c + 1"
"nd": 16900993525017809877161661439
"nd_hex": "0x369c2c96d9717828806ad3ff"
"nd_bit": "2^94 - 2^91 - 2^89 + 2^87 + 2^85 - 2^82 + 2^78 - 2^76 - 2^74 + 2^71 + 2^69 - 2^67 - 2^64 - 2^61 - 2^59 + 2^57 - 2^55 - 2^52 + 2^49 - 2^47 - 2^43 + 2^37 + 2^35 + 2^31 + 2^23 - 2^20 - 2^18 - 2^16 - 2^14 + 2^12 + 2^10 - 1"
"r2": 114882357249
"r2_hex": "0x1abf85a801"
"r2_bit": "2^37 - 2^34 - 2^32 - 2^30 - 2^23 + 2^19 - 2^17 - 2^15 + 2^13 + 2^11 + 1"
"znprimroot": 7
- "n": 19807040628566084398385341441
"n_hex": "0x3ffffffffffffffffff62401"
"n_bit": "2^94 - 2^19 - 2^17 + 2^13 + 2^10 + 1"
"n_fac": "2^10 * 3^2 * 5 * 7 * 41 * 1497701363827647448339c + 1"
"nd": 17360155655652345506456544255
"nd_hex": "0x3817fbf3d3c5f7750ae623ff"
"nd_bit": "2^94 - 2^91 + 2^85 - 2^83 - 2^74 - 2^68 + 2^66 - 2^62 + 2^60 + 2^58 - 2^54 + 2^51 - 2^49 - 2^43 - 2^39 - 2^36 + 2^34 + 2^32 + 2^28 - 2^26 - 2^24 - 2^21 + 2^19 - 2^17 + 2^13 + 2^10 - 1"
"r2": 417500776449
"r2_hex": "0x6134fc4801"
"r2_bit": "2^39 - 2^37 + 2^32 + 2^30 - 2^28 + 2^26 + 2^24 - 2^18 + 2^14 + 2^11 + 1"
"znprimroot": 11
- "n": 1980704
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