Detect functions with the additive property for prime numbers up to a specified limit.

solve.js

function isAdditive(f,x,y){
	return ((f(x) + f(y)) === f(x+y));
}

function everyCombinationOfTwo(arr){
	var toreturn = [];
	arr.forEach(function(first){
		arr.forEach(function(second){
			toreturn.push([first,second]);
		});
	});
	return toreturn;
}

function getAllPrimesUpToLimit(limit){
	var primes = [2];
	var i = 2;
	while(i<=limit){
		if(determineIfPrimeFromList(i,primes)){
			primes.push(i);
		}
		i++;
	}
	return primes;
}

function determineIfPrimeFromList(x, primes){
	for(var i=0;i<primes.length;i++){
		if((x%primes[i])===0){
			return false;
		}
		else if(primes[i]>Math.sqrt(x)){
			return true
		}
	}
	return true;
}

function solve(secret,limit){
	var combos = everyCombinationOfTwo(getAllPrimesUpToLimit(limit));
	for(var i=0;i<combos.length;i++){
		if(!isAdditive(secret,combos[i][0],combos[i][1])){
			return false
		}
	}
	return true;
}

function tests(){
	var assert = require('assert');
	
	//TEST isAdditive
	var additive = function(x){ return 3*x; };
	var notAdditive = function(x) {return x-1; };
	assert.equal(isAdditive(additive,3,5),true, "isAdditive should be true");
	assert.equal(isAdditive(notAdditive,3,5),false, "isAdditive should be false");
	
	//TEST everyCombinationOfTwo
	assert.deepEqual(everyCombinationOfTwo([1,2,3]), [ [1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3] ], "everyCombinationOfTwo([1,2,3])");
	
	//TEST getAllPrimesUpToLimit
	var primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149];
	assert.deepEqual(getAllPrimesUpToLimit(150), primes, "getAllPrimesUpToLimit(150)");
	
	//TEST determineIfPrimeFromList
	assert.equal(determineIfPrimeFromList(5, [2,3,5,7]), true, "determineIfPrimeFromList with prime number in list");
	assert.equal(determineIfPrimeFromList(4, [2,3,5,7]), false, "determineIfPrimeFromList with nonprime number less than last");
	assert.equal(determineIfPrimeFromList(14, [2,3,5,7]), false, "determineIfPrimeFromList with nonprime number greater than last");
	
	//TEST solve
	assert.equal(solve(additive,500), true, "solve() should have returned true");
	assert.equal(solve(notAdditive,900), false, "solve() should have returned false");

	//VISIBLE TEST
	function secret(x){
		return (6*x);
	}
	console.log('secret(12): ' + secret(12));
	console.log('secret(22): ' + secret(22));
	console.log('secret(12+22): ' + secret(12+22));
	console.log('secret(12) + secret(22): ' + (secret(12) + secret(22)) );
	console.log('Is Additive? = ' + solve(secret));
}

tests();