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arXiv · 2504.15658

Improved Upper Bound on Brun's Constant Under GRH

Lachlan Dunn
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Abstract

Brun's constant is the summation of the reciprocals of all twin primes, given by $B=\sum_{p \in P_2}{\left( \frac{1}{p} + \frac{1}{p+2}\right)}$. While rigorous unconditional bounds on $B$ are known, we present the first rigorous bound on Brun's constant under the GRH assumption, yielding $B < 2.1594$.

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Lachlan Dunn. 2025-04-22. Improved Upper Bound on Brun's Constant Under GRH. https://arxiv.org/abs/2504.15658

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