Primes between consecutive powers

Michaela Cully-Hugill

doi:10.1016/j.jnt.2022.12.002

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arXiv · 2107.14468

Primes between consecutive powers

Michaela Cully-Hugill

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Abstract

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 $n\geq 1$. 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.

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Michaela Cully-Hugill. 2021-07-30. Primes between consecutive powers. https://doi.org/10.1016/j.jnt.2022.12.002

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