// Function to check if a number is perfect
function isPerfect(number) {
	if (number <= 1) {
		return false;
	}

	let sum = 1;

	for (let i = 2; i <= Math.sqrt(number); i++) {
		if (number % i === 0) {
			sum += i;

			if (i !== number / i) {
				sum += number / i;
			}
		}
	}

	return sum === number;
}

// Slow version: checks every number
function generatePerfectNumbersSlow(countLimit) {
	let count = 0;
	let number = 1;

	while (count < countLimit) {
		if (isPerfect(number)) {
			console.log(number);
			count++;
		}

		number++;
	}
}

// Function to check if a number is prime
function isPrime(number) {
	if (number <= 1) {
		return false;
	}

	for (let i = 2; i <= Math.sqrt(number); i++) {
		if (number % i === 0) {
			return false;
		}
	}

	return true;
}

// Fast version: uses Mersenne primes
function generatePerfectNumbersFast(countLimit) {
	let count = 0;
	let p = 2;

	while (count < countLimit) {
		const mersenneNumber = Math.pow(2, p) - 1;

		if (isPrime(mersenneNumber)) {
			const perfectNumber = Math.pow(2, p - 1) * mersenneNumber;
			console.log(perfectNumber);
			count++;
		}

		p++;
	}
}

// Keep the slow demonstration small enough to finish in a reasonable time.
const countLimit = 4;

console.log("Slow version:");
console.time("Slow version time");
generatePerfectNumbersSlow(countLimit);
console.timeEnd("Slow version time");

console.log("--------------------");

console.log("Fast version:");
console.time("Fast version time");
generatePerfectNumbersFast(countLimit);
console.timeEnd("Fast version time");

console.log("end");