058.js

// Starting with 1 and spiralling anticlockwise in the following way, a square 
// spiral with side length 7 is formed.

//    37 36 35 34 33 32 31
//    38 17 16 15 14 13 30
//    39 18  5  4  3 12 29
//    40 19  6  1  2 11 28
//    41 20  7  8  9 10 27
//    42 21 22 23 24 25 26
//    43 44 45 46 47 48 49

// It is interesting to note that the odd squares lie along the bottom right 
// diagonal, but what is more interesting is that 8 out of the 13 numbers lying 
// along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.

// If one complete new layer is wrapped around the spiral above, a square 
// spiral with side length 9 will be formed. If this process is continued, what
// is the side length of the square spiral for which the ratio of primes along 
// both diagonals first falls below 10%?

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 minSpiralSize(percent) {
    var numbers  = [1];
    var size = 1;
    var totalNumbers = 1;
    var totalPrimes = 0;
    while ((totalPrimes/totalNumbers) >= (percent/100) || !totalPrimes) {
        size += 2;
        totalNumbers += 4;
        var diagonal = 4;
        while (diagonal--) {
            if (isPrime(size*size - (size-1)*diagonal)) {// Numbers on diagonal
                totalPrimes++;
            }
        }
    }
    return size;
}

console.log( minSpiralSize(10) );