A published paper or arXiv preprint answers the main question of Erdős Problem #970 (theorem erdos_970 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

The problem, as stated in formal-conjectures (Apache 2.0):

Let h(k) be Jacobsthal's function, defined to as the minimal m such that, if n has at most k prime factors, then in any set of m consecutive integers there exists an integer coprime to n. Determine the order of magnitude of h(k). In particular, is it true that h(k) \ll k^2? The bound h(k) \ll k^2 was proved by an internal OpenAI model in September 2026 [OAI26a]; see the linked Lean proof. The order of magnitude of h(k) remains open.

References formal-conjectures lists for this problem (a starting point, not evidence):

• [FGKMT18] Ford, Kevin and Green, Ben and Konyagin, Sergei and Maynard, James and Tao, Terence, Long gaps between primes. J. Amer. Math. Soc. (2018), 65-105.
• [Iw78] Iwaniec, Henryk, On the problem of {J}acobsthal. Demonstratio Math. (1978), 225--231.
• [OAI26a] OpenAI, A quadratic bound for Jacobsthal's function. OpenAI Math Release preprint (2026).