Prime time

摘要

Prime numbers are beautiful and fascinating - and an infuriating puzzle. Easy to define, yet rowdy and disordered, the primes have no evident pattern. The more of them you list, the more erratic they seem to be. Over the centuries, people have hunted for ways to find out which numbers are prime and which are not, and yet the best tests ever devised are so slow that even our ever-faster computers don't help much. A millionfold increase in computer speed just adds a few digits to the size of the numbers that can be handled. Mathematicians would dearly love a truly efficient way to find primes, and that needs brainpower, not computer power. At last, we are on the brink of such a test, thanks to the brains of Manindra Agrawal and his students Neeraj Kayal and Nitin Saxena at the Indian Institute of Technology, Kanpur. And their work might mean more than just bigger game for prime-number hunters. Powerful codes based on primes are used to keep internet shopping and banking private and secure, and although the new test does not directly undermine the security of these codes, it hints that in the future our online dealings might be susceptible to an attack from an unexpected direction.