Work

Improved Upper Bound on Brun’s Constant Under Grh

Year: 2025

Type: article

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

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972725100233

Author: LACHLAN DUNN

Institution: The University of Queensland

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,550

Funder: University of Queensland