Claims

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2026_01_19_tang: Theorem 1.2 of the note by Quanyu Tang and ChatGPT-5.2 Thinking: f(n) is at most the ceiling of n^(12/17+epsilon) for large n; the thread states the exponent 30/43 through Guth and Maynard. Superseded by the (log n)^2 bound.

2026_03_31_alexeev_putterman_sawhney_sellke_valiant: Theorem 2.1 of Alexeev, Putterman, Sawhney, Sellke and Valiant (arXiv 2026): f(n) is at most (24/(pi^2-6)+o(1))(log n)^2 for large n and at least (1/2+o(1)) log n along a sequence; unrefereed, the order of f(n) stays open.

2026_09_03_bae: An arXiv preprint with a Lean 4 proof that f(n) exceeds (1/2 - o(1)) log n log log n / log log log n infinitely often, so f(n) = O(log n) fails; the order of f(n) stays open between that bound and (log n)^2.

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