# The Primes Are Infinite

The Primes Are Infinite

The prime numbers, 2, 3, 5, 7, 11, …, are integers divisible only by themselves and one. Euclid's Elements IX:20 proves the primes are infinite. "Consider any finite set of primes. Multiply all of them together and add one. The resulting number is not divisible by any of the primes in the finite set we considered, because dividing by any of these would give a remainder of one". This Demonstration allows you to study Euclid's method with various sets of primes.