Jakub Niksinski, Rutgers University

Abstract

How large can the gap between consecutive primes be relative to their magnitude? We will discuss some heuristics and prove a result of Westzynthius, who showed that prime gaps can be much larger than the average gap. If time permits, I will sketch improvements to these ideas due to Ford, Green, Konyagin, Maynard, and Tao which allowed them to grab $10,000 from Erdős's pocket.