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

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