Create an algorithm, in JS, to list all primes smaller than or equal to N

Question

I need to create an algorithm in Javascript, to list all prime numbers less than or equal to a given number.

function primeNumber (num){
    var num = 0;
    for (var i = 0; i <= num; i++){
        if ((num % 1 === 0) && (num % num === 0)){
            return (primeNumber(i));
        }
    }
}
console.log(primeNumber(num));

Where am I going wrong?

Answer 1

Concept:

To identify a prime number we must divide it successively by prime numbers such as: 2, 3, 5. . . and check whether the division is exact (where the rest is zero) or not exact (where the rest is non-zero).

• If the rest of the division is zero the number is not prime.
• If no rest is zero, the number is prime.

Simple example in code where the function primeNumbers will interact from 0 to the amount of numbers and the isPrime will check if the same is actually prime number:

function primeNumbers(num) {
  let numbers = new Array();
  for (var i = 0; i <= num; i++) {
    if (isPrime(i)){
      numbers.push(i);
    }
  }
  return numbers;
}
function isPrime(num) {
  for(let i = 2; i <num; i++)
    if(num % i === 0) {
        return false
    };
  return num > 1;
}
console.log(primeNumbers(13));

where the operation will bring all the numbers between the number given.

Answer 2

The most common definition is that "a number is prime if it is divisible by 1 and by itself" or else "it is all the number with two and only two divisors, itself and the unit". So, for example, the number 7 is prime because it is divisible only by 1 and by 7.

1. By definition the number 2 is a prime number so we must test from the divisor 2.
2. If in function primeNumber there is some divisor that the rest of the division is equal to 0 he’s not cousin and we can stop with the check.

function primeNumber(num) {
    for (var divisor = 2; divisor < num; divisor++) 
    if (num % divisor == 0) return false;
    return true;
}

var determinadoNumero = 50;

for (var i = 2; i < determinadoNumero; i++) if (primeNumber(i)) console.log(i);

the number 2 is the only prime number that is even.