041.js

// We shall say that an n-digit number is pandigital if it makes use of all 
// the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital 
// and is also prime.

// What is the largest n-digit pandigital prime that exists?

function isPrime(n) {
    if (n < 2) return false;
    var q = Math.floor(Math.sqrt(n));
    for (var i = 2; i <= q; i++) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

function permutate(array, callback) {
    function p(array, index, callback) {
        function swap(a, i1, i2) {
            var t = a[i1];
            a[i1] = a[i2];
            a[i2] = t;
        }
        if (index == array.length - 1) {
            callback(array);
            return 1;
        } else {
            var count = p(array, index + 1, callback);
            for (var i = index + 1; i < array.length; i++) {
                swap(array, i, index);
                count += p(array, index + 1, callback);
                swap(array, i, index);
            }
            return count;
        }
    }
    return p(array, 0, callback);
}

// 7 digits? An educated guess
permutate([7,6,5,4,3,2,1], function(arr){
    var num = parseInt(arr.join(''), 10);
    if (isPrime(num)) console.log(num);
});