The result formalizes and extends Maynard’s 2013 work on small gaps between primes, incorporating the Polymath8b refinement that reduced the bound from 600 to 246, and is organized in the public Lean library PrimeGapsLib with 246 as its flagship theorem.

The achievement is framed within AI-driven mathematics, drawing comparisons to Sphere-Packing formalizations and highlighting ongoing debates about the reliability and interpretability of AI-generated proofs.

The formalization pipeline follows three stages: drafting a labeled blueprint with dependencies, generating machine-checkable Lean 4 proofs built on Mathlib, and assembling these into PrimeGapsLib, including a self-contained verification challenge for independent cross-checks.

Ken Ono describes the 246 bound as the current threshold of human knowledge in prime number theory, underscoring its significance and the promise of AI-assisted formal proofs.

Axiom Math has produced a machine-checked Lean 4 proof that infinitely many prime pairs differ by no more than 246, verified via its AxiomProver system and published by August 17, 2026.

The work is presented as a milestone in AI-assisted mathematical formalization, building a reusable infrastructure to support future research in mathematics and potential broader verification tasks in software, finance, and security.

Beyond the 246 bound, the library also formalizes the 600 bound and includes a verification exercise relying solely on Mathlib, with a Lean comparator tool allowing external verification; the full verify may take hours, while the reduced version runs in minutes.