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# rizalp/JavaScript Sieve Of Atkin.js

Created May 3, 2013 11:49
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 = true; sieve = 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);

### kramtark commented Jun 23, 2014

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

### rizalp commented Sep 25, 2014

@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.

### axelduch commented Feb 22, 2015

@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 :)

### scolladon commented Aug 13, 2015

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

### farskid commented Jul 15, 2016

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