060.js

// The primes 3, 7, 109, and 673, are quite remarkable. By taking any two
// primes and concatenating them in any order the result will always be prime.
// For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of
// these four primes, 792, represents the lowest sum for a set of four primes
// with this property.

// Find the lowest sum for a set of five primes for which any two primes
// concatenate to produce another prime.

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 nthPrime(n) {
    var num = 1;
    var i = 0;
    while (i < n) {
        num++;
        while (!isPrime(num)) {
            num++;
        }
        i++;
    }
    return num;
}

var nthPrimeMemo = (function(){
    var memo = [];
    return function(n) {
        var num = memo[n];
        if (typeof num === 'undefined') {
            num = nthPrime(n);
            memo[n] = num;
        }
        return num;
    };
})();

function concatenable(a, b) {
    return isPrime(parseInt('' + a + b, 10)) && isPrime(parseInt('' + b + a, 10));
}

function findLowestSetOfPrimes(limit) {
    var primes = [];
    var i, j, k, l, m;
    for (i = 1; i < limit; i++) {
        primes[0] = nthPrimeMemo(i);

        for (j = i+1; j < limit; j++) {
            primes[1] = nthPrimeMemo(j);
            if (!concatenable(primes[0], primes[1])) continue;

            for (k = j+1; k < limit; k++) {
                primes[2] = nthPrimeMemo(k);
                if (!concatenable(primes[1], primes[2])) continue;
                if (!concatenable(primes[0], primes[2])) continue;

                for (l = k+1; l < limit; l++) {
                    primes[3] = nthPrimeMemo(l);
                    if (!concatenable(primes[2], primes[3])) continue;
                    if (!concatenable(primes[1], primes[3])) continue;
                    if (!concatenable(primes[0], primes[3])) continue;

                    for (m = l+1; m < limit; m++) {
                        primes[4] = nthPrimeMemo(m);
                        if (!concatenable(primes[3], primes[4])) continue;
                        if (!concatenable(primes[2], primes[4])) continue;
                        if (!concatenable(primes[1], primes[4])) continue;
                        if (!concatenable(primes[0], primes[4])) continue;

                        console.log( primes );
                    }
                }
            }
        }
    }
}

findLowestSetOfPrimes(2000);