Improved bounds on Brun's constant

TL;DR

This paper refines the numerical bounds on Brun's constant, narrowing the range based on improved computational methods, thus advancing our understanding of twin primes.

Contribution

The authors provide significantly tighter unconditional bounds on Brun's constant, improving previous estimates by approximately 13%.

Findings

Lower bound of Brun's constant is 1.840503.

Upper bound of Brun's constant is 2.288513.

The bounds are improved by about 13% over previous results.

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.