Geodesic
Large gaps between consecutive prime numbers
Kevin Ford1 ; Ben Green2 ; Sergei Konyagin3 ; Terence Tao4
1 University of Illinois at Urbana-Champaign Urbana, IL
2 Mathematical Institute Oxford England
3 Steklov Mathematical Institute Moscow, Russia
4 University of California Los Angeles CA
Annals of mathematics, Tome 183 (2016) no. 3, pp. 935-974.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $G(X)$ denote the size of the largest gap between consecutive primes below $X$. Answering a question of Erdős, 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.
DOI : 10.4007/annals.2016.183.3.4

Kevin Ford 1 ; Ben Green 2 ; Sergei Konyagin 3 ; Terence Tao 4

1 University of Illinois at Urbana-Champaign Urbana, IL
2 Mathematical Institute Oxford England
3 Steklov Mathematical Institute Moscow, Russia
4 University of California Los Angeles CA 
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Kevin Ford; Ben Green; Sergei Konyagin; Terence Tao. Large gaps between consecutive prime numbers. Annals of mathematics, Tome 183 (2016) no. 3, pp. 935-974. doi : 10.4007/annals.2016.183.3.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.3.4/

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