# Brun’s constant

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

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

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).

Title Brun’s constant BrunsConstant 2013-03-22 13:20:01 2013-03-22 13:20:01 bbukh (348) bbukh (348) 8 bbukh (348) Definition msc 11N36 msc 11N05 BrunsPureSieve