Ad Astra Errans

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Twin prime conjecture and the Pentium division bug — The Endeavour

No one knows whether there is a largest pair of twin primes. The twin prime conjecture says that there are infinitely many pairs of twin primes, but the conjecture has not been proven.


If there were only finitely many twin primes, the sum would have finitely many terms and hence a finite sum. But the sum might converge even though it has infinitely many terms. On the other hand, if we could show that the sum diverges, we’d have a proof of the twin prime conjecture. Viggo Brun showed that the sum does converge. Its sum, known as Brun’s constant, is a little more than 1.9.

In 1994, Thomas Nicely was studying Brun’s constant when he found that his computer incorrectly computed 1/824633702441 beyond the eighth significant figure. Nicely had discovered the infamous Pentium division bug.

No tenía ni idea de cómo se había descubierto aquel bug de los Pentium que tantos chascarrillos generó, que fueron tantos que lo más llamativo de este post es el dato sobre la frecuencia de aparición del fallo:

The error was estimated to occur once in every 9 billion divisions. (I doubt any large program has ever been written that is as bug-free as the buggy Pentium chips.)

Ciertamente, dudo que haya un software que falle con menos frecuencia que ese hardware.