Claims

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2026_01_05_van_doorn: Van Doorn's Theorem 1 (Integers 26 (2026), #A7) gives max_m f(n,m) minus f(n,n) above 0.36 n log n / log log n for all large n, answering Problem 711's second question yes; refereed.

2026_07_11_kominers: Kominers's note of 11 July 2026 claims liminf (F(n) - f(n,n))/(n log n) at least 1/e for F(n) = max_m f(n,m), a stronger yes to Problem 711's second question than van Doorn's; an arXiv preprint, unreviewed.

2026_07_29_chen_korsky: Chen and Korsky's preprint (v1 by Chen, 29 July 2026) bounds F(n) = max_m f(n,m) between n exp((log 2/2 - o(1)) log n/log log n) and n^(4/3+o(1)), which with Erdős–Pomerance gives Problem 711's comparison; unreviewed.

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