Brun's constant

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 Brun's sieve.