Some explicit results on the sum of a prime and an almost prime

Daniel R. Johnston; Valeriia V. Starichkova

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arXiv · 2208.01229

Some explicit results on the sum of a prime and an almost prime

Daniel R. Johnston·Valeriia V. Starichkova

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Abstract

Inspired by a classical result of R\'enyi, we prove that every even integer $N\geq 4$ can be written as the sum of a prime and a number with at most 395 prime factors. We also show, under assumption of the generalised Riemann hypothesis, that this result can be improved to 31 prime factors.

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Daniel R. Johnston, Valeriia V. Starichkova. 2022-08-02. Some explicit results on the sum of a prime and an almost prime. https://arxiv.org/abs/2208.01229

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