First Day Issue
"Discovering the largest known Prime Numbers"
What has this worldwide network of fast and powerful (and not-so-fast, not-so-powerful) digital computers discovered?
Well ... they have discovered, after years of unimaginable computational efforts, Things which always, eternally existed.
They have discovered Things previously discovered perhaps millions of years ago, by other Sentients and their Great Machines elsewhere in the Milky Way Galaxy.
Vleeptron's bumper sticker promises Really Big Integers.
And Vleeptron delivers.
M45 and M46 -- the 45th and 46th, in increasing size, Mersenne Prime Numbers -- have just been discovered and verified, and are a bit on the Unique side.
A few years ago, the Electronic Frontier Foundation offered a prize of U$ 100,000 for the discovery of the first Prime Number which, in its full expansion, has more than 10,000,000 decimal digits.
10,000,000 is a completely arbitrary target. $100,000 is a completely arbitrary prize. Mathematically, a Prime with 10,000,000 decimal digits has nothing special which a Prime with 27,931,422 decimal digits, or one with 3882 digits, doesn't have.
But we Humans of Earth not only usually have ten fingers, but we are a Simple & Childlike Race, and this Prize Contest reflects the philosophy of KISS:
Everybody easily recognizes and grasps lots of Zeroes. Everybody easily grasps Money, and an amount of it with lots of Zeroes.
So the achievement which won the $100,000 check wasn't truly Special or Amazing.
But you can buy a Lexus or a Jaguar with the check anyway.
GIMPS, the brainchild of Mr. George Woltman (one of my heroes), is the world's first network of ordinary PCs, connected via the Internet, to connect enough unused or underused computing power to solve such computationally massive problems -- in this case, discovering and verifying the Largest Prime Number known on Earth.
I love to run GIMPS on my PC. After downloading the software, you never have to think about it again. Leave your PC powered up While-U-Sleep, and you can completely forget it, while it secretly and silently crunches big numbers, automatically Web-zapping intermediate results to Mother. Then Mother zaps another problem to my PC, while she does the same thing to hundreds of thousands of other ordinary PCs and mainframes all over the Planet.
Back at Mother Central, she stitches together all the Small Answers into the Final Big Answer. And year after year, GIMPS discovers the world's biggest known Prime Number. And moves on to find bigger ones.
There is a rich Human and Historical Romance to this Quest. Since the Ancient Greeks, since the Pythagorean Mystery Cult, the greatest mathematicians of every generation have been mesmerized by and seduced into learning the Secrets of the Primes, and squeezing the next record-breaking Prime from these secrets.
This is the Realm not just of Pythagoras, Plato, Eratosthenes and Euclid, but the Realm of Gauss, of Fermat, of Reimann, of Euler.
This is Number Theory. This is Die Mengenlehre.
And because there is an Infinity of Prime Numbers -- Euclid proved that around 300 BCE -- the Quest will never stop. Humans will never get a grip, humans will never grow so Wise or so Sensible that they can control themselves and stop looking for the next World's Biggest Prime.
And now I will shut up and share The Wonderful News, straight from GIMPS:
Titanic Primes Raced
to Win $100,000
San Diego CA and Orlando FL, September 15, 2008 -– Researchers have discovered the two largest known prime numbers, a whopping 12,978,189 and 11,185,272 digits long, as part of a 12-year-old, world-wide volunteer computing project, the Great Internet Mersenne Prime Search ("GIMPS").
The primes can be written shorthand as
(2^37,156,667) - 1
The larger number qualifies for a U$100,000 research award, most of which GIMPS will donate to the University of California, Los Angeles (UCLA), and to charity.
In recognition of every GIMPS participant's contribution, credit for the qualifying prime goes to "Edson Smith, George Woltman, Scott Kurowski, et al", and the other to “Hans-Michael Elvenich, George Woltman, Scott Kurowski, et al".
A nearly decade-long competition for a $100,000 award from the Electronic Frontier Foundation ended closely when the larger prime surfaced on a UCLA computer managed by Edson Smith, just two weeks before the second prime was found by Hans-Michael Elvenich’s computer, in Langenfeld near Cologne, Germany.
Both are among the 100,000 computers in GIMPS PrimeNet, a "grass-roots supercomputer" as Science magazine describes it, which has been running continuously since 1996 and performs 29,000,000,000,000 calculations per second. Had Elvenich’s prime been discovered first, it would have qualified, instead.
“We're proud to be participants in GIMPS and grateful to the UCLA Mathematics Department for providing computational resources to the project,” said Edson Smith, Computing Manager. Hans-Michael Elvenich, a German electrical engineer and prime number enthusiast, adds, “After four years of searching for a prime on GIMPS, finally a great success!”
"These exciting discoveries are literally at the Internet’s ‘electronic frontier’," says PrimeNet inventor, Scott Kurowski, a software technologist in San Diego, California. “Developing technologies and methods to apply the incredibly vast power of cooperative research computing is why the Electronic Frontier Foundation set up their grand challenge awards. It’s serious research, but fun and educational, too.”
GIMPS founder George Woltman in Orlando, Florida said, "In addition to congratulating and gratefully acknowledging the vast contributions of our hundreds of thousands of participants over the years, we're committed to giving $25,000 to charity, $50,000 to UCLA for its part in the discovery, and most of what's left to other GIMPS prime discoverers." He adds, "Our research project will soon offer the chance to achieve the next challenge, the $150,000 award for an immensely more difficult 100-million-digit prime. All you need to participate is our free software download, and a lot of patience!”