Prime Number Checker

About this tool

A prime number has exactly two divisors: 1 and itself. Primes are the atoms of arithmetic - every whole number is either prime or built by multiplying primes - and they guard modern life, since internet encryption relies on giant primes that are practically impossible to factor.

This checker tests your number by trial division: it tries dividing by every integer up to the square root. No divisor found means prime; the first divisor found proves composite - and the tool shows it, so you learn something either way.

How to use

Enter any whole number from 2 upward and press Check Prime.

You get an instant verdict: prime, or not prime with its smallest divisor and the factorisation (for example, 100 = 2 x 50). It handles the numbers homework and curiosity throw at it in milliseconds.

The math behind it

To test n, try divisors from 2 up to the square root of n. If none divides evenly, n is prime - because any factor larger than the square root would pair with one smaller than it, which we already checked.

Checking up to sqrt(n) instead of n itself is the key optimisation: testing 10,007 needs only 100 trial divisions, not 10,005.

Frequently asked questions

Related tools