How will a blank-slate AI first prove the infinitude of primes?

Question

See this market for a description of the kind of AI I am talking about.

There are several proofs of Euclid's theorem - the fact that there are infinitely many primes. This question resolves to whichever proof described on the Wikipedia page (at time of market creation) best captures the approach of the AI when it eventually does this.

Close date updated to 2029-12-31 5:59 pm

Manifold Markets · Answer

Per Manifold Markets prediction market, Euclid's Proof, followed by Saidak's proof by construction and Erdős's Proof are most likely. See the market for live updates (7 traders, as of Jun 3, 2025).