Goldbach's conjecture

golsbach.js

/* Goldbach's conjecture in JavaScript
 *
 * author: Igor Hercowitz
 */


function isPrime(n) {
   if (n % 2 === 0) return false;

   var sqrtn = Math.sqrt(n)+1;
 
   for (var i=3; i < sqrtn; i+=2) {

      if (n % i === 0) return false;
   }

   return true;
}

function primeList(a) {
   if (isPrime(a)) return a; else return false;
}

function generateNumbers(initial) {
    var num = (initial % 2 === 0)?(initial -1):initial;
    var list = []
    for (var i = num; i > 3; i-=2)
        list.push(i);
    list.push(3,1);
    return list;

}

function goldbach(initial, list) {
    var pairs = [];
    while (list.length >0) {
       var item = list.shift();
       var itemPairIndex = list.indexOf(initial - item);
       if  (itemPairIndex !== -1) {        
         var itemPair = list.splice(itemPairIndex,1)
         pairs.push(item+"+"+itemPair);
       }          
    }
    return pairs;
}

var initial = 40000;
print(initial+" can be represented as: "+(goldbach(initial, generateNumbers(initial).filter(primeList))));