Brun’s constant

Brun’s constant is the sum of the reciprocals of all twin primes

$$B=\sum _{\begin{array}{c}p\\ p+2\text{ is prime}\end{array}}\left(\frac{1}{p}+\frac{1}{p+2}\right)\approx 1.9216058.$$

Viggo Brun proved that the constant exists by using a new sieving method, which later became known as Brun’s sieve (http://planetmath.org/BrunsPureSieve).