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February 08, 2013
Volunteer grid computing is in the news again. The distributed computing project known as GIMPS (Great Internet Mersenne Prime Search) has tracked down the largest known prime number after a five-year hunt. Over 17 million digits in length, the number is most easily represented as 2 multiplied by itself 57,885,161 times, minus one.
The Great Internet Mersenne Prime Search (GIMPS) was created in January 1996 by MIT graduate George Woltman with the goal of identifying Mersenne primes using his software Prime95 and Mprime. Now in its 17th year, GIMPS is the longest continuously-running project of its kind. At its peak, the volunteer grid employs 360,000 CPUs, with a top output of 150 trillion calculations per second.
Interestingly, the search for the biggest Mersenne Prime has created a rivalry of sorts between University of Central Missouri and the University of California Los Angeles. This most recent discovery was made by volunteer Curtis Cooper's computer, one of several University of Central Missouri machines engaged in the search. It's the third record prime for the university, where Dr. Cooper is a professor. Their earlier discoveries took place in 2005 and 2006.
Then in 2008 UCLA mathematicians unearthed a 12,978,189 digit prime number. They held onto that record for five years, until the University of Central Missouri came back with the next biggest Mersenne prime.
As this progression demonstrates, not only are Mersenne primes rare, but each successive one gets harder and harder to find. The proof itself took 39 days of continuous computing. Results were independently validated by three different researchers in four separate verification tests.
The Prime Objective
A prime number is a positive integer that can only be divided by one and itself. The prime series starts out 2, 3, 5, 7, 11, 13, and so on. The integer 6 would not be a prime because it is divisible by 2 and 3.
A Mersenne prime is expressed as 2 raised to the power of "P" minus 1, where P is also a prime. Examples of Mersenne primes are 3, 7, 31, and 127, which corresponds to P = 2, 3, 5, and 7 respectively.
According to GIMPS, "Mersenne primes have been central to number theory since they were first discussed by Euclid in 350BC. The man whose name they now bear, the French monk Marin Mersenne (1588-1648), made a famous conjecture on which values of P would yield a prime. It took 300 years and several important discoveries in mathematics to settle his conjecture."
As of this latest discovery, there are now 48 known Mersenne primes. GIMPS has found the last 14 of them.
Computing for a Cause
Volunteer computing relies on the principles of grid computing to allow average netizens to contribute computational resources to a variety of causes. The projects – and there are lots of them – harness the idle processing power of thousands of machines (most often personal computers or university systems) operated by volunteers who have installed a software client on their systems.
Besides GIMPS, other popular projects include SETI@home, Folding@home and the World Community Grid. But these are just a small sampling of the many noteworthy candidates.
Most are strictly volunteer endeavors, but some do provide incentives, and GIMPS is one that does. The project offers two discovery awards: currently set at $3,000 – for numbers with fewer than 100,000,000 digits – and $50,000 – for the first prime discovered having at least 100,000,000 digits. The discovery made by Dr. Cooper's machine (which located a 17,425,170-digit prime) is eligible for the $3,000 award.
The monies for the second and more-substantial award level would actually come from the Electronic Frontier Foundation. As part of its Cooperative Computing Awards project, EFF is providing $150,000 to the first "Internet user" to locate a 100 million digit prime number. GIMPS participants agree in advance that if their computer is the one to identify the next winner, they will split the money with the GIMPS foundation (to be used for future awards) and with a mathematics-related charity.
Prime hunting is no mere mathematical navel gazing, there are implications in higher math theory. Prime numbers are also important to public key cryptography, widely-used to secure online transactions.
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