Factorising numbers into their constituent primes may sound esoteric, but the one-way nature of the problem—and of some other, closely related mathematical tasks—is the foundation on which much modern encryption rests. Such encryption has plenty of uses. It defends state secrets, and the corporate sort. It protects financial flows and medical records. And it makes the $2trn e-commerce industry possible. Without it, credit-card details, bank transfers, emails and the like would zip around the internet unprotected, for anyone so minded to see or steal.
Nobody, however, is certain that the foundation of all this is sound. Though mathematicians have found no quick way to solve the prime-factors problem, neither have they proved that there isn’t one. In theory, any of the world’s millions of professional or amateur mathematicians could have a stroke of inspiration tomorrow and publish a formula that unravels internet cryptography—and most internet commerce with it.