Changes

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

'''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)

:<math>B_2 = \left(\frac{1}{3} + \frac{1}{5}\right)

[[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.

[[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:Prime Numbers]]

[[Category:Number Theory]]