Primes in almost all short intervals

Abstract

The author sharpens a result of Jia (1996), showing that the interval $[n,n+n^{\frac{1}{21.5}+\epsilon }]$ contains prime numbers for almost all $n$. Watt's mean value bound, a delicate sieve decomposition and more accurate estimates for integrals are used to good effect.

arXiv comment28 pages