Find All Primitive Root Modulo of a Prime Number

primitiveRootModulo.js

/*
* Equation for finding the Primitive Root Modulo n:
* cn^n mod p 
* for n = 1 to n = p-1
* This program is a little heavy on the counting, though it seems to work with the current set of Prime Numbers...
*/ 

// a few prime numbers for testing:
const primeNumbers = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281];
// console.log(primeNumbers.length); // check size

// prime number to test (choose from array):
const p = primeNumbers[59]; // 59 is currently max

// calculate modulus for candidate number
function calcModFor(candidate) {
	let primitives = [];
	for (let i = 1; i < p; i++) {
		let primitive = Math.pow(candidate, i) % p; // hopefully we won't catch a Math.pow() infinity problem here :p
		primitives.push(primitive);
	}
	primitives.sort();
	return testRoot(primitives);
}

// if this test finds two equal numbers in the array, then the candidate number is not a Primitive Root Modulo of p
function testRoot(pArray) {
	let isPrimRoot = false;
	for (let i = 0; i < pArray.length; i++) {
		if (pArray[i] === pArray[i+1]) {
			break;
		}
		isPrimRoot = true;
	}
	return isPrimRoot;
}

let rString = ""; // for the presentation...

// check all numbers from 1 to p-1 and check if it's a Primitive Root Modulo of p
let rpNumbers = [];
for (let i = 2; i < p; i++) {
	let isPrimRoot = calcModFor(i);
	// there are fewer numbers that aren't primitive roots than are, so let's focus on the exceptions
	if (!isPrimRoot) {
		rpNumbers.push(i);
	}
}

// presentation:
console.log("Not a Primitive Root of #"+p+":");
for (let i = 0; i < rpNumbers.length; i++) {
	if(i < rpNumbers.length-1) {
		rString = rString + rpNumbers[i] + ", ";
	} else {
		rString = rString + rpNumbers[i] + ".";
	}
}
console.log(rString);

So I'm not a mathematician, but I wanted to try out Diffie-Hellman Key Exchange, but in order for it to work, it seems you need to find a number that is the Primitive Root Modulo of p. So since I don't like doing the math in my head, I set out to write a small program that could do it for me in Node.js. (Why Node.js? Because it's what I know...)

To run:
Edit line 13 to the prime number you want [0-59].
Open terminal and do $ node primitiveRootModulo.js

Or maybe I got the whole thing wrong :p gonna look through it again tomorrow...

...or never.