The recent debacle concerning Intel's faulty Pentium chip surfaced because of computations on Brun's constant performed by Thomas Nicely of Lynchburg College in Virginia. The Pentium had a hardware flaw in its floating point arithmetic that causes certain divisions involving long strings on ones to give incorrect answers that will surface once in every billion or so calculations of reciprocals. (This one in a billion error cost Intel about a billion dollars.) Nicely was estimating Brun's constant, named after the Norwegian Mathematician Viggo Brun who investigated some of its properties in 1909. This number is the sum of the reciprocals of prime pairs. That is
The current estimate of Brun's Constant (1.90216054...) is based on a computation of all primes up to 100 Billion and of the 224,376,048 pairs of twin primes that occur among them. This was due to Richard Brent of the Australian National University. Prime pairs are quite mysterious and little is known about them. It is not known, for example whether there are infinitely many though it is conjectured that this is true.
In order to extend the estimates Nicely performed all his calculations twice by different algorithms. (One using the Pentium chips floating point arithmetic and the other avoiding it.) This is quite standard since there is a long history of bugs showing up in these kinds of very extensive computations. Previously paging errors in the Cray supercomputers had shown up in large scale computations of Pi and now Cray uses such calculations as pert of its testing procedures. The two answers Nicely got differed after the tenth digit and this put a red flag. Eventually after considerable detective work Nicely discovered that the Pentium chip was giving incorrect reciprocals for the twin primes 824,633,702,441 and 824,633,702,443 and the rest, as they say, is history.