Folkman's theorem and the primes
Number Theory
2026-05-19 v3 Combinatorics
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.
Cite
@article{arxiv.2509.12025,
title = {Folkman's theorem and the primes},
author = {David J. Fernández-Bretón},
journal= {arXiv preprint arXiv:2509.12025},
year = {2026}
}
Comments
6 pages, minor changes to the second version