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LETTER from LONDON |
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BIG PAYOFF |
 "NYAH, NYAH, MR. JOHNSON! YOU DID NOT COME UP WITH THE RIGHT TEN MILLION DIGIT NUMBER. YOU DO NOT QUALIFY FOR THE JACKPOT !!!" |
Primes search heading
for 10 million digits
By MICHAEL JOHNSON
of TheColumnists.com
Twenty years ago--and I want credit for this--I invited a famous French scientist to write a piece for my magazine imagining what could be accomplished if thousands of computers were linked up and put to work on the same task. I wanted to call the piece “The Brain as Big as the Planet.” I had even commissioned an illustration.
The scientist rejected the idea as too fanciful. The poor guy seriously lacked imagination, and I knew it, but the story died.
Today several huge tasks are being solved by doing just what I thought made such obvious sense, combining the idle computing power of hundreds of thousands of home and office computers to attack big problems: unscrambling radio signals from space, searching for gigantic prime numbers, and sorting through pharmaceutical formulae that might eventually cure AIDS. All these programs invite amateur computer users to install free software and join in the respective search.
The biggest project is
SETI (Search for Extra-terrestrial Intelligence), monitoring
radio energy from space. The SETI people got together last week
in Cambridge, Massachusetts, to assess their progress after more
than four years of processing signals. This is a project that
has used at various times a grand total of 4 million computers.
SETI gets the imagination going. Occasional patterns have emerged
but no little green men as yet. Just in case, documentation includes
section titled “What to do if ET calls.”
In its own way, a different project is equally exciting--the
use of power from more than half a million computers over the
past eight year period to identify so-called Mersenne prime numbers.
The search has now found 40 Mersenne primes, the latest of unimaginable
length, more than 7 million digits. A prize of $100,000 will
go to the person on whose screen the first prime over 10 million
appears. With so many computers at work on the search, it could
be discovered by yearend or at some point in 2005.
I wanted to know how much power was being sucked out of these underutilized computers, so I asked the co-organizer of GIMPS, George Woltman of Orlando. He made it simple:
“The virtual machine's sustained throughput is currently 13,978 gigaflops, or 1161.2 CPU years' computing time per day. For the testing of Mersenne numbers, this is equivalent to 499 Cray T916 supercomputers, or 249.5 of Cray's most powerful T932 supercomputers, at peak power. As such, PrimeNet ranks among the most powerful computers in the world.”
For the free GIMPS software and more information, go to www.mersenne.org.
Such numbers excite computer programmers and mathematicians like nothing else. The “thrill of the conquest” keeps the project going and going, expanding steadily each year, says Woltman.
Who can envision a 10-million-digit number? It would take six months to write it out in longhand and if printed would require about 20 books. And it would be useless in the world as we know it today. I call it the math equivalent of art for art’s sake.
Joining in such a project is about the last thing I expected to do at this late stage of my education. I have always been a mathophobe, like about 80 percent of the population. But GIMPS sounded just quirky enough to be interesting. My home computer is now helping with the search, quietly calculating in background day and night, working through my very fast Pentium processor.
Woltman points out that
advances in integrated circuit design have helped speed the search.
A 3 GHz Pentium 4 is 100 times faster than the once-blistering
90 MHz Pentium when GIMPS began in 1996.
All I have had to do to enter this game was load the GIMPS software
and remember to leave the machine switched on for a couple of
years. The software updates my status regularly, and now tells
me I have one chance in 191,196 of winning the 100 grand. Seems
a long shot but it beats the British lottery which offers one
chance in 14 million.
Does everyone remember what a prime is? Probably not. It’s a number that can be divided only by 1 or by itself, for example 2,3,5,7,11,13,19. All primes were intellectual curiosities in the world of pure math until recently. But the demand for safe use of credit cards on the internet has now brought the primes into their own. They provide the backbone of internet cryptology. The primes have entered the commercial world in a big way.
In parallel with GIMPS, a recent book on primes that I wrote about for TheColumnists.com last January has now hit 10,000 hardcover sales in Britain--“extremely good,” understates the PR man at Fourth Estate. The author, Marcus du Sautoy, is equally modest but is still delighted.
The GIMPS project and the book, “The Music of the Primes,” seem to be feeding off each other. Author du Sautoy tells me he always knew there was a “real appetite to find out about the magical world of mathematics.” His book is being translated into German, Italian, Greek, Japanese, Korean and Hebrew.
Du Sautoy and Woltman do not work together but separately they have been instrumental in bringing excitement to a subject that usually defies dramatization. Du Sautoy believes math has “something mystical about it that intrigues people.”
Du Sautoy’s publishing phenomenon has now made him a math superstar. He finds himself in such demand for guest lecturing that he can hardly keep up. His website (www.musicoftheprimes.com) is aimed at attracting young people to math, and his guest lectures to them feature himself alternating from the blackboard to the trumpet. He says he is trying to bring students “some of the really great mathematical music that’s out there beyond the boring arithmetic scales of the classroom”.
The nature of numbers being
infinite, the GIMPS search will not stop at 10 million. Chat
rooms associated with the project reveal that math enthusiasts
are already looking at how to tackle billion-digit prime. The
prize for that will be $1 million.
Woltman knows this search is not about money. What makes him
happy is the sense that young people are being attracted to serious
math. “Several times a year, I get an email from a student
or parent about how GIMPS has furthered a student's interest
in math. In the long run, this could be GIMPS’ greatest
impact.”
©2004 by Michael Johnson. The cartoon is from IMSI's Master
Clips Collection, 1895 Francisco Blvd. E., San Rafael, CA, 94901-5506,
USA.
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