---
title: "Prime number checker — free, runs in your browser"
description: "Test whether a number is prime, and get its factors if it is not. Free, no sign-up, and nothing you enter leaves your browser."
url: https://atoneplace.net/tools/prime-number-checker/
site: "At One Place"
---

# Prime number checker

Test whether a number is prime, and get its factors if it is not.

## How it works

Tests a number for primality and, when it is composite, shows its prime factorisation.

Testing by trial division only needs divisors up to the square root. If a number has a factor larger than its square root, it must also have a matching one below it, so anything above that point has already been checked. That is why testing a number near a million takes a thousand steps rather than a million.

Two facts worth knowing. One is not prime, by definition rather than by accident — if it were, every number would have infinitely many factorisations and the fundamental theorem of arithmetic would fail. And two is the only even prime, which makes it the odd one out in a way that catches people.

Primes thin out but never run out. Euclid proved there are infinitely many around 300 BC, with an argument short enough to fit in a paragraph: multiply any finite list of primes together, add one, and the result is divisible by none of them.

> This tool runs entirely in your browser. Nothing you enter is sent to a server, logged or stored, and the page keeps working with the network disconnected.

## Common questions

### Is 1 a prime number?

No, by definition. A prime has exactly two distinct divisors; one has only itself. Excluding it is what makes prime factorisation unique.

### What is the largest known prime?

They are Mersenne primes of the form 2^p − 1, found by distributed search, and the record has passed 40 million digits. New ones are found every few years.

### Why only check up to the square root?

Because any factor above the square root pairs with one below it, so it would already have been found.

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## Sources

- Calculated on this page — At One Place (/about/)