I don't get squaring loop index in prime number function

Question

Below are my functions that sum up all prime numbers that are below a given maxNum .

I don't understand why the for loop in the isPrime function doesn't work when using j <= num instead of j ** 2 <= num .

 function sumPrimes(maxNum) { let sum = 0; for (let i = 2; i <= maxNum; i++) { if (isPrime(i)) { sum += i } } return sum } function isPrime(num) { for (let j = 2; j <= num; j++) { // when I use j ** 2 <= num it works if (num % j === 0) { return false } } return true } console.log(sumPrimes(20))

Answer 1

if you use j <= num , the loop will count j up to the number itself and then it would match num % j === 0 and return false.

So if num was 17, the loop would be executed with 17 <= 17 which passes and the loop body executes 17 % 17 === 0 so it always returns false, no matter what number you pass in.

you could use j < num instead of j <= num in the loop head which should also work because the number itself is never reached when using the smaller than sign.