Trial division method to find whether a number is prime or composite.

primality.js

/* Primality Test
 * Checks if a given number is prime
 * As inspired by http://www.khanacademy.org/cs/level-1-primality-test/1018672065
 */

function leastfactor(n) {
    var m, i;
    if (n == 0) return 0;
    if (n % 1 || n*n < 2) return 1;
    if (n %2 == 0) return 2;
    if (n %3 == 0) return 3;
    if (n %5 == 0) return 5;
    
    m = Math.sqrt(n);
    
    /*
    factors of 2, 3, and 5 have been eliminated, so LCM(2,3,5)=30
    */
    for (i = 7; i <= m; i += 30) {
        if (n % i == 0) return i;
        if (n % (i+4) == 0) return i+4;
        if (n % (i+6) == 0) return i+6;
        if (n % (i+10) == 0) return i+10;
        if (n % (i+12) == 0) return i+12;
        if (n % (i+16) == 0) return i+16;
        if (n % (i+22) == 0) return i+22;
        if (n % (i+24) == 0) return i+24; 
    }
    return n;
}

/*
invariant: x is a number >= 2
*/
var isprime = function(x) {
    if (x == leastfactor(x)) {
        return true;
    } else {
        return false;
    }
};