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).

Title	Brun’s constant
Canonical name	BrunsConstant
Date of creation	2013-03-22 13:20:01
Last modified on	2013-03-22 13:20:01
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	8
Author	bbukh (348)
Entry type	Definition
Classification	msc 11N36
Classification	msc 11N05
Related topic	BrunsPureSieve