Axiom Math Claims New Record Bound of 212 on Prime Gaps

Ashvin Swaminathan posted that Axiom Math lowered the bound on gaps between primes from 240 to 212, building on Stadlmann's recent work. He stated that the result was formally verified by AxiomProver relative to existing literature. Carina Hong, Alberto Alfarano, François Charton, and Scott Kominers amplified the claim on X. François Charton described a human-AI collaboration among number theorists, applied mathematicians, and AxiomProver that used substantial compute. The linked Axiom post states that infinitely many prime pairs differ by 212 or less. Hong framed the work as progress toward the Twin Prime Conjecture.