Open, in the site's label, which attaches to the pair of questions. The second question is answered yes: van Doorn's Theorem 1 (Integers 26 (2026), #A7, a refereed journal) gives $\max_mf(n,m)-f(n,n)>0.36\,n\log n/\log\log n$ for all large $n$; it is an accepted partial claim on its claim page (van Doorn, 2026), which settles the second of the problem's two parts; the derived standing stays open while the first is unsettled. The first question is open: the best published bound is Erdős and Pomerance's Theorem 4, $f(n,m)\le4n([\sqrt n]+1)$ for all $m,n$ (1980), so $\max_mf(n,m)\ll n^{3/2}$; a preprint first posted in July 2026 states, in the abstract of its revision of 13 August 2026, $\max_mf(n,m)\le n^{4/3}\exp(O(\log n/\log\log n))$, not held and not refereed, a pending claim on Chen and Korsky's claim page (2026). For the lower side, $\max_mf(n,m)\ge f(n,n)\gg n\sqrt{\log n/\log\log n}$ (Theorem 2 of 1980), van Doorn's $n\log n/\log\log n$, and two 2026 preprints claiming $(1/e-o(1))n\log n$ and $n\exp((\tfrac{\log2}2-o(1))\log n/\log\log n)$, the last two pending claims on Kominers's claim page (2026) and Chen and Korsky's claim page (2026), each of which also answers the second question. This is a bounded negative finding for the first question, not a certificate of openness. Erdős offered a prize for each of the two questions in 1992, and the site's prize converts the two offers together (below).