IMPROVED UPPER BOUND ON BRUN’S CONSTANT UNDER GRH

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 $B < 2.1594$ .