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return array of primes below limit using Sieve of Atkin Algorithm
http://en.wikipedia.org/wiki/Sieve_of_Atkin
#JavaScript #primes
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function sieveOfAtkin(limit){ | |
var limitSqrt = Math.sqrt(limit); | |
var sieve = []; | |
var n; | |
//prime start from 2, and 3 | |
sieve[2] = true; | |
sieve[3] = true; | |
for (var x = 1; x <= limitSqrt; x++) { | |
var xx = x*x; | |
for (var y = 1; y <= limitSqrt; y++) { | |
var yy = y*y; | |
if (xx + yy >= limit) { | |
break; | |
} | |
// first quadratic using m = 12 and r in R1 = {r : 1, 5} | |
n = (4 * xx) + (yy); | |
if (n <= limit && (n % 12 == 1 || n % 12 == 5)) { | |
sieve[n] = !sieve[n]; | |
} | |
// second quadratic using m = 12 and r in R2 = {r : 7} | |
n = (3 * xx) + (yy); | |
if (n <= limit && (n % 12 == 7)) { | |
sieve[n] = !sieve[n]; | |
} | |
// third quadratic using m = 12 and r in R3 = {r : 11} | |
n = (3 * xx) - (yy); | |
if (x > y && n <= limit && (n % 12 == 11)) { | |
sieve[n] = !sieve[n]; | |
} | |
} | |
} | |
// false each primes multiples | |
for (n = 5; n <= limitSqrt; n++) { | |
if (sieve[n]) { | |
x = n * n; | |
for (i = x; i <= limit; i += x) { | |
sieve[i] = false; | |
} | |
} | |
} | |
//primes values are the one which sieve[x] = true | |
return sieve; | |
} | |
primes = sieveOfAtkin(5000); |
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