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arXiv · 2509.12025

Folkman's theorem and the primes

David J. Fernández-Bretón
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Abstract

We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as using Hindman's theorem). This adds to the existing literature deriving the infinitude of primes from Ramsey-type theorems.

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David J. Fernández-Bretón. 2025-09-15. Folkman's theorem and the primes. https://doi.org/10.1016/j.disc.2026.115227

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