return array of primes below limit using Sieve of Atkin Algorithm

http://en.wikipedia.org/wiki/Sieve_of_Atkin #JavaScript #primes (original) (raw)

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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 \|
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);