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Claim. Write $L(x)$ for the length of the longest interval $I\subseteq[x,2x]$ with $\omega(n)>\log\log n$ for every $n\in I$, the quantity of Problem 452. The report states that

$$L(x)\le\exp\Bigl((1+o(1))\frac{\log x}{\log\log x}\Bigr),$$

proved by a Richert-type weighted sieve: the weight $w(n)=\eta-\sum_p a_p$ runs over the primes $p$ of a window $[z,y)$ and is tuned so that its total over an interval of length $H\ge\exp((1+o(1))\log x/\log\log x)$ is positive, which forces a point of the interval where $\omega(n)$ falls below $\log\log n$. Patrick White published the report on 2026-07-26 on erdosproblemaday.com, a public ledger of AI-assisted reports on the catalog's problems that names its authors as Patrick White and Claude (Anthropic); the ledger lists this entry as LIVE with a full write-up and no claimed proof, and gives it no outcome label. The entry credits the bound to GPT-5.6 Sol and links that model's transcript for the argument. It restates the lower bound $L(x)\ge(1-o(1))\log x/(\log\log x)^2$ from the Chinese remainder theorem and calls the gap between the two bounds open.

Covers. The upper bound only. With the lower bound $(1+o(1))\log x/(\log\log x)^2$ of the site's commentary the size of $L(x)$ stays undetermined, and the bound says nothing about whether intervals of length $(\log x)^k$ exist for every $k$.

Depends on. Nothing in this wiki.

Standing. Claimed. The report is not refereed, is not filed on the site's proof-claims tab, and names no reviewer, so it stays claimed; the site labels the problem OPEN (page last edited 28 October 2025). A thread post of 28 September 2026 proves $L(x)\le x^{(1+\varepsilon)/\log\log x}$ for every $\varepsilon>0$ independently, by a Brun sieve, and cites the report; a thread post of 4 July 2026 gives the weaker bound $L(x)\le x^{O(1/\sqrt{\log\log x})}$ by comparing three moments of the count of small prime factors, and reports that Erdős and Graham knew no upper bound. Neither post is a dated manuscript, so neither has a page.