Brun’s constant for prime quadruplets

Brun’s constant for prime quadruplets is the sum of the reciprocals of all prime quadruplets

$$B_4=\sum _{\begin{array}{c}p\\ p+2\text{ is prime}\\ p+6\text{ is prime}\\ p+8\text{ is prime}\end{array}}\left(\frac{1}{p}+\frac{1}{p+2}+\frac{1}{p+6}+\frac{1}{p+8}\right)\approx 0.8705883800.$$

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).