A WebPage of papers that prove Primes Infinite Using Ramsey Theory
VDW and the Primes by Alpoge
Sqs in AP and Infinitely Many Primes by Granville
FLT implies Infinite Primes by Elsholtz
FLT, Schur's Theorem, and Infinitude of the Primes by Gasarch
Slides on Gasarch Proof
The Green-Tao Theorem and the Infinitude of the Primes by Hikmet-Ozcan-Sertbac