return array of primes below limit using Sieve of Atkin Algorithm http://en.wikipedia.org/wiki/Sieve_of_Atkin #JavaScript #primes

JavaScript Sieve Of Atkin.js

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);

Is line 39 missing a var declaration for i? I don't see it defined as such elsewhere. Is this permitted in Javascript?

@kramtark Yes it is permitted. Js is function-scoped, not block scoped like C or Java. So whether we define var or not in the for loop declaration, it doesn't matter because that variable only exist in sieveOfAtkin function...

The only danger, is if you have variable i outside of sieveOfAtkin. It will be overridden.

@rizalp This is not true, and strict mode would throw an error because you are defining window.i as it is never "declared" with the var keyword.

Therefore i pollutes the global scope.

Anyways, thank you for sharing this implementation :)

Why line line 12 y is instanciate with 1 ? Should it not be y = x ?

This a performance friendly implementation as stated in wikipedia. But the output seems to be useless cause indexes of an array as the prime numbers cant be used anywhere.
See this link for a converter I coded to return a list of actual prime numbers.
https://gist.github.com/farskid/3501b1b981607483a46b76d61e092e6e