-
-
Save farskid/3501b1b981607483a46b76d61e092e6e to your computer and use it in GitHub Desktop.
return array of primes below limit using Sieve of Atkin Algorithmhttp://en.wikipedia.org/wiki/Sieve_of_Atkin#JavaScript #primes
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
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; | |
} | |
// This converter make sit possible to get an array of actual prime numbers numbers instead ofa list of falsy and true values whose indexes are the prime numbers itself. | |
function convertSieve(sieve) { | |
var ret = []; | |
sieve.forEach(function(num, index) { | |
if (num) { | |
ret.push(index); | |
} | |
}); | |
return ret; | |
} | |
primes = convertSieve(sieveOfAtkin(5000)); |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment