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 6 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 this 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. But that wasn't the whole story.
Perhaps the best-known example is Fermat's Last Theorem, scribbled in the margin of an old book around 1636 and finally proved by Andrew Wiles in 1994. Fermat wrote that he had found a "marvelous proof" of a negative statement: If you take a whole number and raise it to some power greater than two, he said, it is not possible to write that number as the sum of two nonzero numbers raised to the same power. So, say, 20,736, which is 12 to the fourth power, cannot be written as a sum of two (nonzero) numbers to the fourth power.
A nonmathematician might wonder why anyone would want to prove that. But not only did people want to, they spent 350 years trying. During those years, many mathematicians put together a vast theoretical edifice dealing with such exotic beasts as "elliptic curves," "modular forms" and "Galois representations." The theory served as the base camp from which Wiles set out to get to the peak. It was an impressive conquest, and the methods are proving to be fruitful indeed, but as far as we know the whole thing has no practical use.
