Euclid's theorem

This article is about the theorem on the infinitude of prime numbers. For the theorem on perfect numbers and Mersenne primes, see Euclid–Euler theorem. For the theorem on the divisibility of products by primes, see Euclid's lemma.

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid in his work Elements. There are several proofs of the theorem.