Claims

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1976_01_01_richter: Richter's 1976 Theorem proves liminf q_n/n^2 at least 1/2.84010... = 0.3521... for every sequence of primes with non-decreasing gaps; refereed in Acta Arithmetica, it leaves the limit question open.

2026_09_27_lin: A Lean 4 development published on 27 September 2026 claims liminf q_n/n^2 at least 255255/(295318+G) > 0.864289 for prime sequences with non-decreasing gaps, by a max-plus certificate checked in Lean; the limit question is open.

2026_10_06_satorunet: A write-up posted to the site's proof-claims tab on 6 October 2026 claims liminf q_n/n^2 at least 0.9200 by a computer-certified residue argument, with constraints on a counterexample; the limit question itself is left open.

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