Prime Number Checker
Type any whole number and find out whether it is prime — and if it is not, one of its factors is shown, so you can see exactly why. Numbers up to 15 digits are checked with deterministic Miller-Rabin plus trial division, which is instant for homework numbers and fast well beyond them.
Prime numbers are the atoms of arithmetic: divisible only by 1 and themselves. They drive cryptography, appear in nature (cicada life cycles), and are the endless fascination of number theory — this checker settles any 'is 1,009 prime?' argument in a keystroke.
How to use
- Type any whole number (2 or greater).
- Read the verdict instantly — prime, or composite with a factor shown.
- Try famous cases: Mersenne suspects like 2,147,483,647, or your phone number.
Frequently asked questions
What is a prime number?
A whole number greater than 1 whose only divisors are 1 and itself: 2, 3, 5, 7, 11, 13… Every other number (composites) breaks into prime factors, which is why primes are called the atoms of arithmetic.
Is 1 a prime number?
No — by definition primes need exactly two distinct divisors, and 1 has only one (itself). Mathematicians agreed on this convention precisely so that unique factorization works.
What is the largest known prime number?
The largest known primes are Mersenne primes of the form 2^p − 1 — the record has millions of digits and is found by distributed GIMPS projects. This checker handles everyday numbers up to 15 digits instantly.
Why do primes matter outside math class?
Internet encryption (RSA, Diffie-Hellman) is built on the difficulty of factoring huge composite numbers made of two large primes. Every HTTPS connection starts with prime number mathematics.