A Mathematician Broke a Prime-Number Record. AI Beat It Within Days

On Aug. 31, mathematician Julia Stadlmann of the University of Illinois Urbana-Champaign set a new record on number theory's twin prime conjecture, which holds that infinitely many pairs of primes are just two apart, such as 3 and 5. She narrowed the "prime gap bound" — the gap size guaranteed to repeat infinitely among primes — from 246 to 240, the field's first improvement in more than a decade.

The 246 bound had stood since 2014, built on a 2013 proof by mathematician Yitang Zhang — now at Sun Yat-sen University in China — that some prime gap under 70 million repeats infinitely. Stadlmann, who finished her doctorate under James Maynard at Oxford two years earlier, spent that time combining newer techniques with Zhang's approach, both resting on a "sieve" method that filters out non-primes using different weights.

Her lead didn't last. Within three days, researchers at AI startup Axiom Math built her ideas into a theorem-proving AI system and pushed the bound to 212. Within two hours, OpenAI said its newest large language model — an AI system trained to generate and reason through text, called GPT-6 Astra — had pushed the bound to 186, in a paper released with the model on Sept. 3. OpenAI's Sébastien Bubeck said the company had mainly used a related problem, on the largest prime gaps, to test Astra, exploring the smaller-gap problem as an add-on.

Kevin Ford, Stadlmann's postdoctoral mentor at Illinois, called it "a David-versus-Goliath story where the human gets the gold" — for three days, at least. Mathematician Terence Tao of UCLA, a Fields Medalist, wrote that some AI companies were "abandoning any pretense of gaining human understanding" to chase benchmark results.

Bubeck said OpenAI does not intend to keep pushing on the prime-gap problem. "Our goal is not to preemptively strike and capture all the results possible," he said. "Our strategy is to empower the mathematician."