On Monday, the human species was informed of the discovery of a new highest known prime number. No doubt some of you have already prepared and eaten celebratory feasts. The largest-known-prime record is broken every few years by means of a networked-computing project called GIMPS, the Great Internet Mersenne Prime Search. GIMPS is a beautiful holdover from the old internet, a time when humans were setting out to prove the possibilities for collective exploitation of spare computer resources.
In case you have forgotten, not so long ago, millions of ordinary people unexpectedly found themselves owning calculating machines of ludicrous power, most of which sat idle much of the day — or even from second to second while being used. By downloading a bit of GIMPS software and letting it run in the background, someone who knew nothing of any math could end up receiving credit for advancing the frontier of number theory, and gaining a little corner on immortality.
This effort has, it must be added, little or no practical significance. It doesn’t change anyone’s life to have the information we have gained — namely, that 2136,279,841-1 is not divisible by any smaller integer except itself and 1. If GIMPS folded up tomorrow, as one supposes it eventually will, there would be no specifiable injury to mankind.
But mathematical chimera-chasing of this kind is known to pay off in unexpected ways, and, at a minimum, encourages the development of computing algorithms and approaches that crack open large numbers more efficiently. It’s often observed that number theory was an idle, even artistic activity for millennia until it became important to modern cryptography. The deeper truth might be that it is a very fundamental activity of humankind: if you have a religious bent, you might hypothesize that we exist to increase computing power, to construct automata of an ever-more-godlike character. And, well, it’s happening one way or another.
With that said, there is a slightly sad note to the latest GIMPS landmark, which, in the words of the official press release, “ends the 28-year reign of ordinary personal computers finding these huge prime numbers.” Previous “discoverers” got lucky and won the GIMPS lottery using regular Pentium and Intel Core home computers, although if you owned an especially fast rig, your chances were much better. But the largest-prime chase has now become the preserve of coders exploiting the special abilities of advanced graphics processing units (GPUs), computer chips of the esoteric kind that are currently making Nvidia investors rich.
GPUs were developed to speed up image processing in personal computers and game consoles, but the underlying techniques make them better at any problem which involves fast parallel multiplication of large numbers. This makes GPUs ideal for algorithms which check large candidate primes, as they are for real-world tasks like face recognition and matching DNA sequences in different datasets. Different applications, same math.
So, the main “discoverer” of the new largest prime isn’t a schmuck with an old Pentium grinding out ones and zeroes on his local area network; it’s a gentleman named Luke Durant who used to work for Nvidia, and who pulled together a global “cloud supercomputer” made of expensive GPUs that have idle time not tied up in cryptocurrency mining. The GIMPS-driven prime search is becoming less democratic and old-internet-y, and more an exclusive province of technological sophisticates, which is recognizable as a more general phenomenon — one of those waves of history that sway us back and forth.
National Post