Link of the week - UCLA finds first Mersenne Prime over 10 million digits
On August 23rd, a UCLA computer discovered the 45th known Mersenne prime, 243,112,609 - 1, a mammoth 12,978,189 digit number! The prime number qualifies for the Electronic Frontier Foundation 's $100,000 award for discovery of the first 10 million digit prime number. Congratulations to Edson Smith, who was responsible for installing and maintaining the Great Internet Mersenne Prime Search (GIMPS) software on the UCLA Mathematics Department's computers.
Edson Smith, a system administrator in the Mathematics department at UCLA, says congratulations are due the entire UCLA Mathematics Computing Group. On behalf of the group, he responds to a number of questions about Mersenne Primes and the award via a FAQ. His page is non-technical; all you have to know is that a Prime Number is evenly divisible only by itself and the number 1.
Here's a teaser... but do read the FAQ; it's worth it!
Q. What's a Mersenne Prime?
A. Mersenne Prime numbers all take the form of 2P-1, where P is a known prime. The first Mersenne Prime is 3 because 22 - 1 = 3. Note that the exponent P is a prime number, in this case 2. The next Mersenne Prime is 7 because 23 - 1 = 7, with P being the prime number 3. Next comes 31 (25 - 1), then 127 (27 - 1), followed by 8,191 (213 - 1) and 131,071 (217 - 1). Mersenne Primes get big very fast.
Q. Why are people looking for them?
A. For the same reasons that people climb mountains, sail unknown seas, and explore the cosmos. It's a challenge! It's exciting to push the envelope of Computational Mathematics and to search for something unknown that you believe is out there. As bonus, unlike the explorers of old, we get to sit in comfortable office chairs while we're searching!
This is not to say that there's no mathematical value in Mersenne Primes. They're certainly of value in the field of cryptography, and may have other uses yet to be discovered.
Q. Aside from the challenge, why did you decide to participate?
A. We realized that our large (75 seat) PIC/Math Computer Lab was using only a fraction of its available CPU power. Rather than let all those cycles go to waste, we looked at a number of distributed computing projects, and determined that GIMPS was the best fit for us.
Q. How do you test for them?
A. There are lots of numbers of the form 2P - 1, but only a very few of them are Mersenne Primes. The GIMPS Prime95 program we use makes extensive use of a 75-year-old algorithm called the Lucas-Lehmer Test, widely recognized as the best tool to test for Mersenne Primes.
GIMPS is one of many ongoing efforts in the field of distributed computing, and arguably the most successful. Thousands of people using tens of thousands of computers participate. It can take a single machine months to test just one candidate number, but by harnessing the power of Internet-connected individual computers all over the world, we can make rapid progress.
Smith's text was adapted and reprinted with permission.