Checking Whether a Number Is Prime

This lesson covers checking whether a number is prime in Java, so you understand a basic math algorithm using a loop. It's for anyone searching "Java prime check implementation."

Whether a number is prime (divisible only by 1 and itself) can be determined by checking whether it's divisible by any number from 2 up to its square root. If none of them divide it evenly, it's prime.

The example loops over the range for (int i = 2; i * i <= n; i++), deciding the number isn't prime the moment it finds an i where n % i == 0. Checking only up to the square root works because any larger factor would necessarily be paired with a smaller one you'd have already found.

A common early mistake is not knowing why checking only up to the square root is sufficient. Simply checking every number less than n also works correctly, but limiting it to the square root cuts down wasted calculation and speeds things up.

It's an important mathematical property that underlies cryptography too, and there's also a more advanced technique, the Sieve of Eratosthenes, for efficiently finding many primes at once.

📖 Reference code

public class Main {
    static boolean isPrime(int n) {
        if (n < 2) return false;
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) return false;
        }
        return true;
    }

    public static void main(String[] args) {
        System.out.println(isPrime(17));
        System.out.println(isPrime(18));
    }
}

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