Twin Prime Numbers, Bounded Gaps Between Primes

Abstract

In this thesis an in-depth explanation will be given of the proof Maynard gave in his article. In which the steps of the proofs will be expanded. He used a re?nement on the GPY sieve to study k-tuples and small gaps between primes. This will show that the lim inf (Pn+1 - Pn) < 600, and, by assuming the Elliott-Halberstam conjecture, that lim inf(Pn+1 - Pn) < 12 and lim inf(Pn+2 - Pn) < 600.