# Large gaps between consecutive prime numbers

@article{Ford2014LargeGB,
title={Large gaps between consecutive prime numbers},
author={Kevin Ford and Ben Green and Sergei Konyagin and Terence Tao},
journal={arXiv: Number Theory},
year={2014}
}
• Published 20 August 2014
• Mathematics
• arXiv: Number Theory
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…

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