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arXiv · 1407.7902

Short effective intervals containing primes

Habiba Kadiri·Allysa Lumley
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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 Ramar\'e and Saouter and is used to verify the Ternary Goldbach Conjecture for the integers up to $7.86\cdot 10^{27}$.

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Habiba Kadiri, Allysa Lumley. 2014-07-29. Short effective intervals containing primes. https://arxiv.org/abs/1407.7902

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