What is a prime number?

A prime number is a whole number greater than 1 whose only divisors are 1 and itself. The numbers 2, 3, 5, 7 and 11 are prime; 4, 6, 8 and 9 are not.

Why are 0 and 1 not prime?

By definition a prime must be greater than 1, so 0 and 1 are not prime. 2 is the only even prime number.

How does the checker test for primality?

It uses trial division: it checks whether any whole number from 2 up to the square root of your number divides it evenly. If none do, the number is prime; if one does, it is composite.

Why only check up to the square root?

If a number n has a factor larger than √n, the matching co-factor must be smaller than √n. So any factor would already have been found below the square root, making it enough to test up to √n.

Is 2 really the only even prime?

Yes. Every other even number is divisible by 2 as well as 1 and itself, so it has more than two divisors. That makes 2 the single even prime.

Does this send my number anywhere?

No — the primality test and factorisation run entirely in your browser, and nothing you enter is uploaded.

Prime Number Checker

Q: What does it show for a non-prime number?

It reports the number as composite and shows its prime factorisation — the unique set of primes that multiply to give it, such as 12 = 2² × 3.

Prime number checker

Enter any whole number and instantly see whether it is prime — a whole number greater than 1 divisible only by 1 and itself. When a number is not prime, the tool also shows its prime factorisation, the unique set of prime factors that multiply to give it. Handy for maths homework, number theory and quick checks.

How it works

The checker uses efficient trial division up to the square root of your number:

if n < 2 → not prime
test each d from 2 up to √n
  if any d divides n evenly → composite (n is not prime)
if none divide n → prime

Testing only to √n is enough, because any factor above the square root pairs with one below it. For composite numbers, the same division yields the prime factorisation.

Example

Checking 97: no number from 2 up to √97 ≈ 9.8 divides it evenly, so 97 is prime.

Checking 91: 7 divides it (91 = 7 × 13), so 91 is not prime, with factorisation 7 × 13.

Number	Prime?	Factorisation
2	Yes	—
91	No	7 × 13
97	Yes	—
100	No	2² × 5²

The test runs entirely in your browser, so nothing you enter is ever uploaded.