Improved bounds on Brun's constant

Abstract

Brun's constant is $B={\sum }_{p\in P_2}{p}^{-1}+(p+2{)}^{-1}$, where the summation is over all twin primes. We improve the unconditional bounds on Brun's constant to $1.840503<B<2.288513$, which is about a 13\% improvement on the previous best published result.

11 pages; submitted to the proceedings of the Jon Borwein Commemorative Conference