Distribution of prime numbers;
Explicit estimates;
Prime number theorem;
Riemann zeta-function;
SHARPER BOUNDS;
EXPLICIT;
DENSITY;
ZEROS;
D O I:
10.1016/j.jnt.2022.12.002
中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
This paper updates the explicit interval estimate for primes between consecutive powers. It is shown that there is least one prime between n(155) and (n + 1)(155) for all n >= 1. This result is in part obtained with a new explicit version of Goldston's 1983 estimate for the error in the truncated Riemann-von Mangoldt explicit formula. (c) 2023 Elsevier Inc. All rights reserved.