Proofs that there are infinitely many primes

By Chris Caldwell

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 variationof Euclid's proof. Perhaps the strangest is Fürstenberg's topological proof. Check them out and see which one you like.

• Euclid's Proof (c. 300 BC)
• Furstenberg's Topological Proof (1955)
• Goldbach's Proof (1730)
• Kummer's Restatement of Euclid's Proof
• Filip Saidak's Proof (2005)