Edit in JSFiddle

function isPrime(num) {
    // deal with 0, 1, 2, 3
    if (num <= 3) {
        if (num <= 1) {
            return false;
        }
        return true;
    }
    // deal with multiples of 2 and 3
    if (num % 2 == 0 || num % 3 == 0) {
        return false;
    }
    // test all numbers not divisible by 2 or 3
    for (var i = 5; i < Math.sqrt(num) + 1; i += 6) {
        if (num % i == 0 || num % (i + 2) == 0) {
            return false;
        }
    }
    return true;
}

$("#go").click(function () {
    var candidate = $("#candidate").val() * 1;
    if (isNaN(candidate) || candidate < 0 || candidate > 9007199254740992) {
        $("#answers").append("Cannot test " + candidate.toString() + "<br>");
        return;
    }
    if (isPrime(candidate)) {
        $("#answers").append(candidate.toString() + " is prime<br>");
    } else {
        $("#answers").append(candidate.toString() + " is not prime<br>");
    }
});