Brun's constantBrunsConstant2002-12-27 14:31:492006-11-03 13:32:05DefinitionBrun's sievetwin primes\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}\emph{Brun's constant} is the sum of the reciprocals of all twin primes
\begin{equation*}
B=\sum_{\substack{p\\p+2 \text{ is prime}}} \left(\frac{1}{p}+\frac{1}{p+2}\right)\approx 1.9216058.
\end{equation*}
Viggo Brun proved that the constant exists by using a new sieving method, which later became known as \PMlinkname{Brun's sieve}{BrunsPureSieve}.