Claims

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2004_04_08_green_tao: Theorem 1.1 of Green and Tao (Ann. of Math. 2008) gives infinitely many k-term arithmetic progressions of primes for every k, the yes answer to Problem 219; accepted on the refereed publication and the site's credit.

2026_09_23_openai: Corollary 1.2 of the OpenAI release manuscript of 23 September 2026 (every set with divergent reciprocal sum contains progressions of every length) applied to the primes through the divergence of the sum of 1/p; a second route, accepted on its built Lean proof and Mathlib's divergence theorem.

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