Increasing and decreasing prime gaps

2016/04/06 by Daniel Shiu, Shiu, D. K. L.
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1604.01761

openalex publication_date 2016/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p_n denote the nth prime and g_n:=p_n+1-p_n the nth prime gap. We demonstrate the existence of infinitely many values of n for which g_n>g_n+1>⋯>g_n+m with m≫ logloglog n and similarly for the reversed inequalities. In doing so we settle a conjecture of Erdös for the case m=2.

Citations

• Dense clusters of primes in subsets

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