In 1919 Brun showed that the sum of the reciprocals of the twin primes converges to a sum now called Brun's Constant:
(1/3 + 1/5) + (1/5 + 1/7) + (1/11 + 1/13) + (1/17 + 1/19) + ...
By calculating the twin primes up to 1014 (and discovering the infamous Pentium bug along the way), Nicely heuristically estimated Brun's constant to be 1.902160578. More recently he has improved this estimate to 1.9021605824 by using the twins to 1.6.1015.
Related pages (outside of this work)
- The sum of the reciprocals of all primes diverges
- Thomas Nicely's homepage with links to some of his work