# Brun’s constant for prime quadruplets

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

 $B_{4}=\sum_{\begin{subarray}{c}p\\ p+2\text{ is prime}\\ p+6\text{ is prime}\\ p+8\text{ is prime}\end{subarray}}\left(\frac{1}{p}+\frac{1}{p+2}+\frac{1}{p+6% }+\frac{1}{p+8}\right)\approx 0.8705883800.$

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).

Title Brun’s constant for prime quadruplets BrunsConstantForPrimeQuadruplets 2013-03-22 16:06:23 2013-03-22 16:06:23 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11N05 msc 11N36 Brun’s constant for prime quadruples Brun’s constant for prime quartets