paper

Folkman's theorem and the primes

arXiv:2509.12025 · doi:10.1016/j.disc.2026.115227

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.

6 pages, minor changes to the second version