Checking for prime numbers is a common task in mathematics and computer science. It's also pretty common in coding interviews and challenges. Let's see how to check if a number is prime and how to generate prime numbers up to a given number.

Check if a number is prime

To check if an integer is a prime number, we can simply use a for loop. Inside the loop we can check if the number is divisible by any number from 2 to the square root of the given number. If such a number is found, we can return false. If no such number is found, we can return true, unless the number is less than 2.

const isPrime = num => {
  const boundary = Math.floor(Math.sqrt(num));
  for (let i = 2; i <= boundary; i++) if (num % i === 0) return false;
  return num >= 2;
};

isPrime(11); // true

NOTE

This code snippet may be fairly inefficient for very large numbers. Optimizations are possible, but they are beyond the scope of this article.

Generate primes up to a given number

Using the Sieve of Eratosthenes algorithm, we can generate primes up to a given number. The algorithm works as follows:

• Generate an array from 2 to the given number.
• Use Array.prototype.filter() to filter out the values divisible by any number from 2 to the square root of the provided number.

const primes = num => {
  let arr = Array.from({ length: num - 1 }).map((x, i) => i + 2),
    sqroot = Math.floor(Math.sqrt(num)),
    numsTillSqroot = Array.from({ length: sqroot - 1 }).map((x, i) => i + 2);
  numsTillSqroot.forEach(x => (arr = arr.filter(y => y % x !== 0 || y === x)));
  return arr;
};

primes(10); // [2, 3, 5, 7]