Well over 2000 years ago Euclid proved that there were infinitely many
primes. Since then dozens of proofs have been devised and below we
present links to several of these. (Note that [Ribenboim95] gives eleven!)
My favorite is Kummer's variation of Euclid's proof.
Perhaps the strangest is Fürstenberg's topological
proof. Check them out and see which one you like.