Claimed: a pending full claim would settle it. The site labels the problem OPEN (page last edited 1 October 2025; accessed 2026-09-04). The OpenAI release of September 2026 claims a proof: for every $\epsilon>0$ infinitely many $n$ have $g(n)>n^{1-\epsilon}$, from a count of $x^{1-o(1)}$ primes $p$ with $2x<p\le5x$ whose predecessor $p-1$ has no prime factor above $x^{\delta}$, for every fixed $\delta>0$. The release has no Lean for it and no outside review is known, so the claim is pending on OpenAI 2026. The fixed exponents proved before it have partial claim pages: Baker and Harman's refereed $g(n)>n^{0.7039}$ for infinitely many $n$, which settles every $\epsilon\ge0.2961$, on Baker and Harman 1998, and Lichtman's $g(n)\ge n^{0.7156}$ for infinitely many $n$, strict by his Theorem 1.1 and the site's best known bound, which settles every $\epsilon\ge0.2844$, on Lichtman 2022.