Geodesic
Small gaps between primes
James Maynard1
1 Magdalen College, Oxford, Oxford OX1 4AU, United Kingdom
Annals of mathematics, Tome 181 (2015) no. 1, pp. 383-413.

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

We introduce a refinement of the GPY sieve method for studying prime $k$-tuples and small gaps between primes. This refinement avoids previous limitations of the method and allows us to show that for each $k$, the prime $k$-tuples conjecture holds for a positive proportion of admissible $k$-tuples. In particular, $\liminf_{n}(p_{n+m}-p_n)<\infty$ for every integer $m$. We also show that $\liminf(p_{n+1}-p_n)\le 600$ and, if we assume the Elliott-Halberstam conjecture, that $\liminf_n(p_{n+1}-p_n)\le 12$ and $\liminf_n (p_{n+2}-p_n)\le 600$.
DOI : 10.4007/annals.2015.181.1.7

James Maynard 1

1 Magdalen College, Oxford, Oxford OX1 4AU, United Kingdom 
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James Maynard. Small gaps between primes. Annals of mathematics, Tome 181 (2015) no. 1, pp. 383-413. doi : 10.4007/annals.2015.181.1.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.181.1.7/

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