I shall post occasional mathematical 'factoids' here. Please feel free to add your own.
Brun's constant and the Pentium bug: Viggo Brun's constant is the sum of the reciprocals of the twin primes. He proved that this (probably infinite) sum converged to a constant in 1919.
(Twin primes are the prime numbers that only differ by two, such as 5 and 7 or 71 and 73. There are conjectured to be an infinity of twin primes, though this has yet to be proven. A large pair are:
33218925 * 2^169690 +/- 1, which have 51,090 digits each.
The only number that appears in two twin pairs is 5 [3, 5] [5, 7])
Brun's constant is 1/3 + 1/5 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + ... and has a value of approximately 1.902161
While using a computer to calculate Brun's constant in 1994, Thomas Nicely discovered the infamous 'Pentium Bug'. The chip gave occasional errors when performing floating point division operations due to five errors encoded into a lookup table inside the chip. This cost Intel millions to fix.
