Long gaps between primes

By Kevin Ford, Ben Joseph Green, Sergei V. Konyagin, James Maynard, Terence Tao. 2014

98 citations recorded by the source corpus.

Let $p_n$ denotes the $n$-th prime. We prove that $$\max_{p_{n+1} \leq X} (p_{n+1}-p_n) \gg \frac{\log X \log \log X\log\log\log\log X}{\log \log \log X}$$ for sufficiently large $X$, improving upon recent bounds of the first three 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 R\"odl nibble method.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/6da0a1d0a630e84a045350ea98f5be6d2c3b131b

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Large gaps between consecutive prime numbers (2014, background): “results on linear equations between primes). As it turns out, the techniques of this paper and of that in [26] may be combined to establish further results on large prime gaps; see the followup paper [11] to this work and to [26]. Based on a probabilistic model of primes, Crame´r [6] conjectured tha”