GPT-5.6 reportedly broke a 2018 record on gaps between prime numbers

A pure mathematics record held since 2018 by five leading number theorists has fallen to a language model, according to one of the field’s own researchers.

What was reported

Stanford mathematician Jared Lichtman reported on August 30, 2026 that GPT-5.6 has broken the record on large gaps between primes, improving the bound by a factor of roughly log base 3 of n over the previous best result. That result was set in 2018 by Kevin Ford, Ben Green, Sergei Konyagin, James Maynard and Terence Tao, a lineup that includes two Fields medalists; Maynard’s 2022 medal partly recognized his work on exactly this family of problems.

Lichtman added that the result has been formalized in Lean by Alexeev, which would mean a computer has verified every logical step. That has not been confirmed publicly. According to Traictory, the erdosproblems.com page records only that the problem statement is formalized, and a formalized statement is not a formalized proof. Thomas Bloom, who maintains the site, has published an exposition of the proof, but no part of it has been independently verified.

The problem

Prime gaps ask a deceptively simple question: how long can the empty stretches between consecutive prime numbers get? Progress on the lower bound for large gaps is measured in decades, and the 2018 improvement had stood for eight years.

Why it matters

Frontier models are no longer only reproducing known mathematics but claiming to extend it, and checking those claims is now the bottleneck. Until this proof is formalized or independently verified, the open question is still whether the model really proved something, and after that, how far the pattern extends into problems mathematicians actually care about.