Claims

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1978_01_01_iwaniec: The Corollary of Iwaniec's 1978 paper on Jacobsthal's problem, C(r) << r^2 log^2 r, gives h(k) << (k log k)^2; a refereed upper bound, while the order of h(k) and h(k) << k^2 stay open on this source.

2014_12_16_ford_green_konyagin_maynard_tao: Display (1.2) of the 2018 long-gaps paper, through (1.3) at x = p_k, gives h(k) >> k (log k)^2 log_3 k/log_2 k, a refereed lower bound stronger than the site's display; the order of h(k) stays open.

2026_09_25_openai: OpenAI's theorem h(k) << k^2/(log log 3k)^2 answers the displayed question h(k) << k^2 yes; a partial claim accepted on the Lean declaration erdos_970_quadratic (h(k) <= C k^2) built and audited here; order of h(k) open.

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