Large gaps between primes
Given a prime p, the Prime Number Theorem tells us the average gap between primes around p, while the Twin Prime Conjecture gives the smallest gap that can occur infinitely many times. We explore the other end of the spectrum and ask how large these gaps can get infinitely often. We give an exposition of the 2018 paper "Long Gaps Between Primes" by Ford, Green, Konyagin, Maynard, and Tao. Using methods from analytic number theory, sieve theory, and hypergraph covering, the authors proved a new lower bound on the large gaps between consecutive primes, improving a previous one made some 80 years ago.