Euclid's Theorem/Corollary 1

Corollary to Euclid's Theorem
There are infinitely many prime numbers.

Also known as
This result is often referred to as Euclid's Theorem.

But himself did not explicitly state that there is an infinite number of primes, just that it was impossible to create a list containing them all.

Some sources refer to it as Euclid's second theorem, his first being Euclid's Lemma for Prime Divisors.