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arXiv · 2006.04547

The Hardy-Littlewood conjectures on the twin primes and the binary Goldbach problem are true

Maurizio Laporta
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Abstract

A celebrated conjecture of Hardy and Littlewood provides with an asymptotic formula for the counting function of the twin primes. We give an unconditional proof of such a formula by means of a finite Ramanujan expansion of the counting function expressed in terms of the von Mangoldt function and its incomplete form. In a completely analogous way, we solve the conjugate conjecture on the representations of any even integer as the sum of two prime numbers.

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Maurizio Laporta. 2020-06-04. The Hardy-Littlewood conjectures on the twin primes and the binary Goldbach problem are true. https://arxiv.org/abs/2006.04547

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