View source for Brun's constant

'''Brun's constant''' is the sum of the reciprocals of [[twin primes]], which converges despite the divergence of the sum of the reciprocals of all primes:

:<math>B_2 = \left(\frac{1}{3} + \frac{1}{5}\right)
+ \left(\frac{1}{5} + \frac{1}{7}\right)
+ \left(\frac{1}{11} + \frac{1}{13}\right)
+ \left(\frac{1}{17} + \frac{1}{19}\right)
+ \left(\frac{1}{29} + \frac{1}{31}\right) 
+ \left(\frac{1}{41} + \frac{1}{43}\right) + \cdots</math>

[[Viggo Brun]] proved this convergence in 1919.  The convergence of this [[series (mathematics)|series]] leaves it unclear whether there are an infinite number of twin primes, one of the great unsolved problems in [[mathematics]].  The scarcity of twin primes as they grow larger enables their reciprocal sum to converge.

[[Category:Number Theory]]