Department of Mathematics and Computer Science
UCM Researchers Repeat Discovery
Contact: Jeff Murphy
WARRENSBURG - 09/15/2006 - Within nine months after they first announced the discovery of the largest known prime number, mathematics researchers at UCM have done it again.
Mersenne Prime of 9.8 Million Digits
Their latest find, a Mersenne prime number with 9.8 million digits, is the closest anyone has come to winning a $100,000 prize in the worldwide Great Internet Mersenne Prime Search. A financial award from Electronic Frontier Foundation will honor the first individual or team to find a 10 million-digit prime.
The UCM discovery is expressed as M32582657, or, in other words, 2 to the 32,582,657th power minus one. It is about 650,000 digits larger than the previous largest Mersenne prime number discovered at Central Missouri. That number, known as M30402457, had more than 9.15 million digits.
Team of UCM Researchers Participate
"What's better than finding one Mersenne prime? Finding two," said Steven Boone, interim dean of the College of Arts and Sciences at UCM. He and Curtis Cooper, professor of computer science, are leading the campus team of researchers who are participating in GIMPS.
"We're getting so close, we think the next one almost has to be over 10 million digits," Boone remarked.
Mersenne Prime Numbers Historic in Nature
Prime numbers are positive integers, greater than one, that can only be divided by themselves and the number one, for example, numbers like 2, 3, 5, 7, and so on. Mersenne primes are part of a special class of rare primes that are named for French monk Marin Mersenne, who studied them more than 300 years ago. In written form, they are expressed as the number 2 raised to the power of "p" minus one, where "p" is also a prime number. The latest number is the 44th discovery of a Mersenne prime.
Originated in Same Computer Lab
Adding to the rarity of discovering two Mersenne primes, the latest number was also found in the same computer lab where the previous largest prime was discovered – a lab in the Department of Communication.
"The chance of this happening once is pretty small, but twice is unbelievable. There's probably a greater chance of getting struck twice by lighting," Cooper joked. He said UCM has participated in GIMPS for more than nine years. Currently there are about 850 computers on UCM's campuses in Warrensburg and Lee's Summit that are running the free PrimeNet software program that is being used by Mersenne prime number researchers across the globe.
46,000 Individuals and 71,000 Computers Participating
"There are more than 46,000 individuals or groups participating in GIMPS, with more than 71,000 computers running the GIMPS software and communicating with the PrimeNet server," Cooper said. He noted that the computations done by the PrimeNet "virtual machine" in a single day are equivalent to the work a Pentium (90MHz) computer would do over 1,800 years.
Research Has Countless Applications
George Woltman, who founded GIMPS in 1996, said Mersenne primes today are most relevant to number theory. He added, however, most GIMPS participants study them for the fun of having a role in real research and the chance of finding a new Mersenne prime. Past Mersenne prime searches have led to important advances in Fast Fourier Transforms (used in countless applications) as well as discovering computer hardware problems via rigorous stress testing.
For More Information
People who want to know more about GIMPS can do so via the web at www.mersenne.org/. Individuals who are interested in obtaining software to participate in the project can also do so by visiting the same web site.