British mathematician E.C. Titchmarsh: “If we can know, it surely would be intolerable not to know.”
It took hundreds of thousands of computers and several years of work, but they got it. “They” are the participants in the Great Internet Mersenne Prime Search. “It” is one more very large prime number, a monster with six million digits, part of a sequence of numbers known as “Mersenne primes” that is expected (but not known) to go on forever.
As mathematical achievements go, this one was fairly minor. It required no theoretical innovation, no conceptual leap; time, persistence, the Internet and lots of computers were enough.
Finding a new Mersenne prime confirms the expectation that it was there to find, but does not give us much more than that. As one of the people involved said last month when the discovery was announced, “It’s a neat accomplishment, but it really doesn’t have any applicability.”
Many great mathematical quests are like this. They are exciting adventures of the mind whose completion takes years of effort by whole communities of mathematicians but whose results are not usually of immediate practical use. This may come as a surprise, since our teachers spent a lot of time telling us that mathematics is important because it is useful.