Prime Number Checker
Check if a number is prime, find its factors, or generate a list of primes.
Frequently Asked Questions
What is a prime number?▼
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13... The number 1 is not prime by definition.
Why is 2 the only even prime?▼
Every even number is divisible by 2. Since 2 is divisible only by 1 and itself, it qualifies as prime. Any other even number has at least three divisors (1, 2, and itself), so none can be prime.
How many prime numbers are there?▼
There are infinitely many primes — proven by Euclid around 300 BC. His proof: assume a finite list, multiply them all together and add 1. That number is either prime itself, or divisible by a prime not in the list. Contradiction.
What is the Sieve of Eratosthenes?▼
An ancient algorithm to find all primes up to a limit. Start with a list 2–N. Mark 2 as prime, cross out its multiples. Move to the next unmarked number, mark it prime, cross out multiples. Repeat until N. All unmarked numbers are prime.