Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claims
2004_04_08_green_tao: Theorem 1.1 of Green and Tao (Ann. of Math. 2008): the primes contain arbitrarily long arithmetic progressions, Problem 3's conclusion for the set of primes; accepted on the refereed publication.
2020_07_07_bloom_sisask: Corollary 1.2 of Bloom and Sisask's 2020 preprint: a set of naturals with divergent reciprocal sum contains infinitely many three-term arithmetic progressions, the case k = 3 of the problem; claimed, with no journal version.
2026_09_23_openai: Corollary 1.2 of the OpenAI release manuscript of 23 September 2026 answers Problem 3 yes; its Lean declaration, pinned by a comparator challenge, was built and audited by this corpus, so accepted.