Geodesic
Long gaps between primes
Ford, Kevin1 ; Green, Ben2 ; Konyagin, Sergei3 ; Maynard, James2 ; Tao, Terence4
1 Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
2 Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom
3 Steklov Mathematical Institute, 8 Gubkin Street, Moscow, 119991, Russia
4 Department of Mathematics, UCLA, 405 Hilgard Avenue, Los Angeles, California 90095
Journal of the American Mathematical Society, Tome 31 (2018) no. 1, pp. 65-105 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

Let $p_n$ denote the $n$th prime. We prove that \[ \max _{p_{n} \leqslant X} (p_{n+1}-p_n) \gg \frac {\log X \log \log X\log \log \log \log X}{\log \log \log X}\] for sufficiently large $X$, improving upon recent bounds of the first, second, third, and fifth authors and of the fourth author. Our main new ingredient is a generalization of a hypergraph covering theorem of Pippenger and Spencer, proven using the Rödl nibble method.
DOI : 10.1090/jams/876

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

1 Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
2 Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom
3 Steklov Mathematical Institute, 8 Gubkin Street, Moscow, 119991, Russia
4 Department of Mathematics, UCLA, 405 Hilgard Avenue, Los Angeles, California 90095 
@article{10_1090_jams_876,
     author = {Ford, Kevin and Green, Ben and Konyagin, Sergei and Maynard, James and Tao, Terence},
     title = {Long gaps between primes},
     journal = {Journal of the American Mathematical Society},
     pages = {65--105},
     year = {2018},
     volume = {31},
     number = {1},
     doi = {10.1090/jams/876},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/jams/876/}
}
TY  - JOUR
AU  - Ford, Kevin
AU  - Green, Ben
AU  - Konyagin, Sergei
AU  - Maynard, James
AU  - Tao, Terence
TI  - Long gaps between primes
JO  - Journal of the American Mathematical Society
PY  - 2018
SP  - 65
EP  - 105
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1090/jams/876/
DO  - 10.1090/jams/876
ID  - 10_1090_jams_876
ER  - 
%0 Journal Article
%A Ford, Kevin
%A Green, Ben
%A Konyagin, Sergei
%A Maynard, James
%A Tao, Terence
%T Long gaps between primes
%J Journal of the American Mathematical Society
%D 2018
%P 65-105
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1090/jams/876/
%R 10.1090/jams/876
%F 10_1090_jams_876
Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence. Long gaps between primes. Journal of the American Mathematical Society, Tome 31 (2018) no. 1, pp. 65-105. doi: 10.1090/jams/876

Cité par Sources :