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arXiv · 1411.6543

Large gaps between consecutive prime numbers containing perfect powers

Kevin Ford·D. R. Heath-Brown·Sergei Konyagin
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Abstract

For any positive integer $k$, we show that infinitely often, perfect $k$-th powers appear inside very long gaps between consecutive prime numbers, that is, gaps of size $$ c_k \frac{\log p \log_2 p \log_4 p}{(\log_3 p)^2}, $$ where $p$ is the smaller of the two primes.

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Kevin Ford, D. R. Heath-Brown, Sergei Konyagin. 2014-11-24. Large gaps between consecutive prime numbers containing perfect powers. https://arxiv.org/abs/1411.6543

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