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Claim. On printed p. 273 of his 1976 paper, after conjecture (7), Erdős writes: "The best that I can show is $n_k>k^2\exp((\log k)^c)$ for a certain $c>0$." Here $n_k$ is the least $n$ such that each of $n+1,\ldots,n+k$ has a prime factor greater than $k$, and $k(n)=\max\{k:n_k\le n\}$, so the bound gives $k(n)\le n^{1/2}\exp(-(\log n)^{c'})$ for some $c'>0$, using $\log k(n)\ge(\log n)^{1/2-o(1)}$ from display (6). The passage is paged at inequality (6) of the library's source card. The same sentence says he cannot show $n_k>k^{2+\epsilon}$, which would give $k(n)\le n^{1/2-c}$.

Covers. The upper bound on $k(n)$ only; neither question of Problem 962 is settled by it.

Depends on. Erdős 1976, for the lower bound used in the translation to $k(n)$.

Standing. Claimed. The paper asserts the bound without proof or reference, and no proof of it has been found in print; the curator's thread post of 3 April 2026 reports it as a claimed proof. The proved upper bound is $k(n)\le(1+o(1))n^{1/2}$, from Tao's thread argument, recorded on the problem page.