On the gaps between consecutive primes

2018/02/07 by Sun, Yu-Chen, Pan, Hao
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1802.02470

Abstract

Let p_n denote the n-th prime. For any m≥ 1, there exist infinitely many n such that p_n-p_n-m≤ C_m for some large constant C_m>0, and p_n+1-p_n≥ (c_mlog nloglog nloglogloglog n)/(logloglog n), for some small constant c_m>0. Furthermore, we also obtain a related result concerning the least primes in arithmetic progressions.

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