Short effective intervals containing primes

Abstract

We prove that if $x$ is large enough, namely $x\ge x_0$, then there exists a prime between $x(1-{\Delta }^{-1})$ and $x$, where $\Delta$ is an effective constant computed in terms of $x_0$. This improves some previous results of Ramaré and Saouter and is used to verify the Ternary Goldbach Conjecture for the integers up to $7.86\cdot 10^{27}$.

to appear in Integers

References in corpus (1)

• Minor arcs for Goldbach's problem

Cited by in corpus (1)

• Primes between consecutive powers