Using an international grid of about 240,000 networked computers, researchers have discovered the largest known prime number.
The number, expressed as 2 to the 24,036,583th power minus 1, has 7,235,733 decimal digits.
Discovered May 15, the number is nearly a million digits larger than the previous largest prime number, which was itself discovered last December.
The find is part of a special class of prime numbers called Mersenne primes.
They are named after Marin Mersenne, a 17th century French monk who first studied the rare numbers 300 years ago, though Euclid first conjectured about them in 350 B.C. The latest number actually is the 41st Mersenne Prime to be discovered.
”It’s like climbing the Mt. Everest of numbers,” says George Woltman, a retired computer programmer and founder of the Great Internet Mersenne Prime Search (GIMPS).
”It’s about making the climb and conquering the mountain.”
Woltman, a long-time IT professional, says it’s also about the power of the grid and finding out how far they can take that power.
”It’s nice to push the envelope of computing power,” he adds. ”It serves as a bench mark for how fast computers are and how far distributed computers have come.”
It’s difficult to grasp the sheer size of this newly discovered prime number.
If you added up all the atoms in the universe, according to Woltman, you’d come up with a number with fewer than 200 digits.
Or if you were trying to type out the whole number and you typed one digit per second 24 hours a day, Woltman says it would take you 83 days to finish it.
Prime numbers, which have long fascinated mathematicians, are integers greater than one that only can be divided by one and itself.
The first prime numbers are 2,3, 5, 7 and 11. The number 2 is the only even prime number.
A Mersenne prime number is a prime that flows from the equation 2 to the P minus 1.
The first Mersenne primes are 3, 7, 31 and 127. This latest Mersenne prime is expressed as 2 to the 24,036,583th power minus 1.
Woltman explains that the Mersenne algorithm makes it easier to find these large prime numbers.
He notes that when you get upwards of 20,000 or 30,000 digits it simply becomes too taxing to find a prime number without an algorithm. It would take too much time and too much computing power to make it feasible.
And the computer grid that is used in GIMPS is quite powerful.
Of the 240,000 computers networked onto the grid, Woltman says 20,000 to 40,000 computers are active at any one time. The grid covers virtually every time zone in the world.
Woltman estimates that the grid, which is comprised of businesses, universities and home users, does 20 trillion calculations a second.
Each computer on the grid runs software that can be downloaded for free from the GIMPS web site: www.mersenne.org.
Every computer tests one or two numbers per month, depending on the amount of power in each system.
The individual computers communicate with a main server, maintained by Scott Kurowski at Entropia, Inc., a Carlsbad, Calif.-based grid computing company.
Josh Findley, a volunteer at the research project, was running the computer that discovered this latest prime number.
Findley is a consultant to the National Oceanic and Atmospheric Administration in La Jolla, Calif. He used a 2.4 GHz Pentium 4 Windows XP computer running for 14 days to prove the prime number.
Tony Reix of Grenoble, France independently verified the find using half of a Bull NovaScale 5000 HPC running Linux on 16 Itanium II 1.3 GHz CPUs for five days.
Woltman and the volunteers at GIMPS are closing in on the big prize.
The Electronic Frontier Foundation is offering a $100,000 reward for the discovery of the first 10-million-digit prime number. This prime number just discovered is 72 percent of the size needed.
Woltman says they’re not far away from hitting that 10-million-digit mark. ”This find was fairly quick — just six months,” he says.
”Before that, it was about a two-year gap. We probably expect to find one every year or every two years.”