Prime Number Checker

Check whether a number is prime and see its factors.

Is 9973 prime?

Yes

It has exactly two divisors: 1 and itself

Twin prime

Palindromic

Nearest prime below

9967

Nearest prime above

10007

Trial division by small primes, then a deterministic Miller-Rabin test.

Primality testing is fast even for huge numbers. Factorising them is not — that asymmetry is what RSA encryption relies on.

What does Prime Number Checker do?

Test any number for primality with an exact deterministic algorithm, and see its prime factorisation when it is composite. It also lists nearby primes and identifies special forms such as twin and Mersenne primes.

How to Use Prime Number Checker

1
Enter a numberAny positive whole number, however large.
2
Read the verdictPrime or composite, with the reasoning.
3
See the factorisationComposite numbers are fully factorised.

Key Features

Deterministic Miller-Rabin test — exact, not probabilistic, for realistic inputs
Full prime factorisation with exponents when the number is composite
Complete divisor list for smaller numbers
Nearest prime below and above
Identifies twin, Mersenne, Fermat and palindromic primes
BigInt arithmetic, so very large numbers are handled exactly

Frequently Asked Questions

Is 1 a prime number?

No. A prime has exactly two distinct positive divisors, and 1 has only one. Excluding it is what makes prime factorisation unique, which the fundamental theorem of arithmetic depends on.

What is the largest prime you can check?

Primality testing works on numbers with hundreds of digits because it uses BigInt arithmetic. Full factorisation is much harder and is practical up to around 10¹⁴ — that difficulty is precisely what RSA encryption relies on.

How does the test work?

Trial division by small primes first, then a deterministic Miller-Rabin test with a fixed witness set proven correct for every value below 3.3 × 10²⁴. That covers anything you can reasonably type in.