// Naive sieve in range 1..sqrt(x)
var isPrime = function(x) {
  for (var i = 2, sqr = Math.floor(Math.sqrt(x)); i <= sqr; i++) {
    if (x % i === 0) {
      return false;
    }
  }
  return true;
}

// Optimized sieve for numbers in range 1..99999, uses 64 checks at max.
var isPrimeFast = (function() {
  // Pre-calculate primes in range 1..sqrt(99999)
  var smallPrimes = [];
  for (var i = 2; i < 316; i++) {
    if (isPrime(i)) {
      smallPrimes.push(i);
    }
  }

  return function(x) {
    var sqr = Math.floor(Math.sqrt(x));
    for (var i = 0; smallPrimes[i] <= sqr; i++) {
      if (x % smallPrimes[i] === 0) {
        return false;
      }
    }
    return true;
  }
})();

var isPalindrome = function(str) {
  for (var i = 0; i < str.length / 2; i++) {
    if (str[i] != str[str.length - i - 1]) {
      return false;
    }
  }
  return true;
}

var findMaxPalindromeProductOfPrimes = function() {
  var bigPrimes = [];

  // Largest to smallest, find a prime
  for (var a = 99999; a >= 10000; a--) {
    if (!isPrimeFast(a)) {
      continue;
    }

    // and check its product with previously found primes,
    // largest to smallest
    bigPrimes.push(a);
    for (var j = 0; j < bigPrimes.length; j++) {
      var b = bigPrimes[j];
      if (isPalindrome('' + (a * b))) {
        // Code enters here when `a` and `b` are the largest possible
        return {
          "value" : a * b,
          "factors" : [a, b]
        }
      }
    }
  }
}

console.log(findMaxPalindromeProductOfPrimes());