Small gaps between primes

• Autores: James Maynard
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 181, Nº 1, 2015, págs. 383-413
• Idioma: inglés
• DOI: 10.4007/annals.2015.181.1.7
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• Resumen

  • 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, lim inf n (p n+m -p n )<8 for every integer m . We also show that lim inf(p n+1 -p n )=600 and, if we assume the Elliott-Halberstam conjecture, that lim inf n (p n+1 -p n )=12 and lim inf n (p n+2 -p n )=600 .