Small gaps between primes

2013/11/19 by James E. Maynard, Maynard, James
Mathematics · #11N05 #11N35 #11N36 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1311.4600

openalex publication_date 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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)

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