The question if there is an upper bound known for Brun's constant was discussed briefly here: <http://gowers.wordpress.com/2009/05/22/what-is-wolfram-alpha-good-for/> but no sure answer was given. 


So I thought I'd ask the question here. Can one get any upper bound for the sum of the reciprocals of the twin primes?



Upper bound on Brun's constant
Crandall and Pomerance, "Prime numbers: a computational perspective" (Google books) says that Brun's constant B, the sum of the reciprocals of the twin primes, is known to be between 1.82 and 2.15.


**edited to add**: I'm aware that this isn't much of a citation. It would be nice if someone who has access to this book could give a better citation. I'd do it, but I'm not near a library today.


