%0 Journal Article
%T Large gaps between consecutive prime numbers
%A Kevin Ford
%A Ben Green
%A Sergei Konyagin
%A Terence Tao
%J Mathematics
%D 2014
%I arXiv
%X Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdos, we show that $$G(X) \geq f(X) \frac{\log X \log \log X \log \log \log \log X}{(\log \log \log X)^2},$$ where $f(X)$ is a function tending to infinity with $X$. Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes.
%U http://arxiv.org/abs/1408.4505v2