Prime Number Checker
Check if a number is prime, find its factors, and list primes up to any limit.
First 50 Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229
Prime Number Facts
- 2 is the only even prime number
- Twin primes differ by 2: (3,5), (11,13), (17,19)…
- There are infinitely many primes (Euclid's theorem)
- The largest known prime (2024) has over 40 million digits
What Makes a Number Prime
A prime number is a whole number greater than 1 whose only divisors are 1 and itself — 2, 3, 5, 7, 11, and so on. Numbers with other divisors are composite. The number 1 is neither prime nor composite by definition, and 2 is the only even prime. This tool checks any number and, if it's composite, lists its prime factors.
How the Check Works
To test whether n is prime, you only need to try dividing it by numbers up to the square root of n. If none divide evenly, n is prime. That shortcut is why checking even large numbers is fast: a divisor larger than √n would have to pair with one smaller than √n, which you'd already have found.
Why Primes Matter
Primes are the building blocks of arithmetic — every whole number factors uniquely into primes — and they underpin modern encryption, where multiplying two huge primes is easy but reversing it is practically impossible. For random values, see the random number generator.