Prime numbers become sparser as numbers grow, but bounding the irregularities is a deep mathematical problem. OpenAI’s quasi-Riemann result would tighten those bounds by restricting where certain mathematical functions can have zeros. The full Riemann hypothesis remains open.

Quanta’s October 19 interviews explain why number theorists are taking the work seriously: it connects existing ideas in an unexpected way, and experts have been simplifying the argument.

The underlying papers appeared in late September and early October. Their verification status differs: the first is reported as Lean-verified; the shorter, weaker October 5 version was still undergoing human scrutiny in this account.

October 5 paper