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arXiv · 1907.06393

Twins almost prime under a Elliott-Halberstam's conjecture

Nathalie Debouzy
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Abstract

We improve Bombieri's asymptotic sieve to localise the variables. As a consequence, we prove, under a Elliott-Halberstam conjecture, that there exists an infinity of twins almost prime. Those are prime numbers $p$ such that for all $\varepsilon>0$, $p-2$ is either a prime number or can be written as $p_1 p_2$ where $p_1$ and $p_2$ are prime and $p_1<X^{\varepsilon}$, and we give the explicit asymptotic.

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BibTeXRIS

Nathalie Debouzy. 2019-07-15. Twins almost prime under a Elliott-Halberstam's conjecture. https://arxiv.org/abs/1907.06393

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