Explicit Interval Estimates for Prime Numbers

Abstract

Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of $(\Delta ,x_0)$ such that for all $x\ge x_0$ there exists at least one prime in the interval $(x(1-{\Delta }^{-1}),x]$.

This version has been updated with corrections to the 2022 paper. 15 pages, comments welcome!

References in corpus (2)

• Accurate estimation of sums over zeros of the Riemann zeta-function
• On an explicit zero-free region for the Dedekind zeta-function

Cited by in corpus (1)

• Primes between consecutive powers