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 $B={\sum }_{p\in P_2}\left(\frac{1}{p}+\frac{1}{p+2}\right)$. While rigorous unconditional bounds on $B$ are known, we present the first rigorous bound on Brun's constant under the GRH assumption, yielding $B<2.1594$.