New Mersenne prime found

arstechnica. ^ | December 20, 2005 @ 10:05AM | Rian J. Stockbower

[Ernest_at_the_Beach]

The Great Internet Mersenne Prime Search (GIMPS)

is possibly the oldest distributed computing project in existence, and has mostly existed on the fringe of the mainstream distributed computing world. Part of this is likely due to the hardcore nerdiness factor of the project. Most people aren't interested in finding huge prime numbers, as potentially useful as they might be. They'd rather fold proteins, search for little green men, or look for spinning neutron stars—all of which have a more tangible appeal than what appears to be numbers for numbers' sake.

There are reasons to look for Mersenne primes, though. There are prizes, for example, though I doubt most people run the project in the hopes of collecting any money. A Mersenne prime is a prime number in the form of 2^P-1. If this number is indeed prime, this will mean that 43 Mersenne primes have been discovered. The GIMPS page itself acknowledges

that "Finding new Mersenne primes is not likely to be of any immediate practical value" and that it is "primarily a recreational pursuit." (Though one could certainly make the case that searching the skies for E.T. is also a recreational pursuit.) In any event, this will be the seventh Mersenne prime that GIMPS has discovered—all seven of which are at the top of the list in terms of size.

In any event, this is an exciting development in the world of numbers. Ars Technica Team Prime Rib is holding down the #2 spot overall. You can check out the team's FAQ if you're interested in joining. Congrats to all of the GIMPS participants, and happy hunting!

[mikrofon]

New Mersenne prime found

Much as I enjoy math puzzles, I prefer a Prime Filet Mignon, thank you...

[Ernest_at_the_Beach]

Background:

Great Internet Mersenne Prime Search

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The Great Internet Mersenne Prime Search, also known as GIMPS, is a prime example of Distributed Computing project at work and no pun intended. It is a collaborative project of volunteers, who use Prime95 and MPrime, software that can be downloaded from the Internet, in order to search for Mersenne prime numbers.

Mersenne primes are named after Marin Mersenne, a French monk and mathematician, who was born in 1588. Mersenne investigated a particular type of prime number: , in which P is an ordinary prime number.

Mersenne primes are much rarer than ordinary primes, of which there are an infinite number. The GIMPS effort, exhaustively searching for possible candidates since 1996, has been responsible for discovering the seven most recent Mersenne Primes. Altogether, in all of history only 43 Mersenne Primes have been discovered.

This project has been rather successful: it has already found a total of 9 Mersenne primes, each of which was the largest known prime at the time of discovery. The largest currently known prime is 2^30,402,457 - 1. This prime was discovered on December 15, 2005. Refer to the article on Mersenne primes for the complete list of GIMPS successes.

The project was founded by George Woltman, who also wrote the prime testing software. The GIMPS project was formed in January 1996. Scott Kurowski wrote the PrimeNet server software that supports the research to demonstrate Entropia distributed computing software, a company he founded in 1997.

Although the GIMPS software has its source code available, technically it is not open source, since it has a restriction which most open source/free software groups find unacceptable – users must abide by the prize distribution terms. This restriction will become meaningless when the EFF prizes are claimed.

For open source alternatives, Glucas and Mlucas are both licensed under the GPL.

Most GIMPS members join the search for the thrill of possibly discovering a record-setting, rare, and historic, new Mersenne prime. All you have to do to be part of it, is to contribute spare or idle CPU cycles. Pretty cool.

If you want to know more, there is a GIMPS FAQ available in this wiki.

[edit]

See also

• Marin Mersenne
• George Woltman
• Scott Kurowski
• Distributed Computing

[edit]

External links

• www.mersenne.org – GIMPS Home Page
• www.mersenneforum.org – GIMPS Forum
• PrimeNet server

[Ernest_at_the_Beach]

Links at post #2 not hot (not working)..

[Ernest_at_the_Beach]

From:

Mersenne prime confirmed

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December 26, 2005 @ 8:07AM - posted by Rian J. Stockbower

Mersenne prime confirmed

Last Tuesday I reported on the potential finding of the 43rd Mersenne prime. Yesterday, Christmas Day, the prime was confirmed and it is 9,152,052 digits long, which means that the $100,000 EFF prize for the first 10 million digit prime is still up for grabs. I'd speculate that the next Mersenne prime will probably be over 10 million digits, so if you're a prize money DCer, now would probably be the time to get involved. ;)

The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain.

The prime was found by the Central Missouri State University team, the most productive Mersenne team in terms of Pentium-90 CPU-years, and the second most powerful team in terms of exponents tested, where the Ars team has them beat. (Don't ask me why P-90 years instead of exponents factored puts them at #1, because it seems backwards to me as well.)

You will be able to order a poster of the prime number relatively soon.

[RightWhale]

Mersenne did a lot more than mathematics. He was the international facilitator and coordinator of the science branch of the Renaissance.

[Lonesome in Massachussets]

(2 raised to 30,402,457)-1.

[Ernest_at_the_Beach]

Fascinating:

The Great Internet Mersenne Prime Search
at
Central Missouri State University

[mikrofon]

But what is the largest known Mersenne Prime for which the exponent of 2 is also a Mersenne?

[socal_parrot]

New Mersenne prime found

This just in...

Alan Greenspan today raised the Mersenne prime a quarter point.

[Ernest_at_the_Beach]

With help from Google found this:

Marin Mersenne

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Who was Marin Mersenne?

You are probably visiting here because of an interest in Mersenne Primes. It was not until the mid 20th century that Mersenne became known primarily for his Prime Number Conjecture. Historically, he was much better known for his correspondence with leading scientists of the day (hence the other Mersenne Mailing List). Interested in optics, he also been called (no pun intended) the Father of Acoustics. Here are some links that will tell you something about the man himself:

*********************************

See link above for more.......

[Lurker]

OK, I have to ask. If a prime number is only divisible by one and itself what the heck is a Mersenne prime and how does it differ from a regular prime number?

That's not explained in the article.

L

[Ernest_at_the_Beach]

But what is the largest known Mersenne Prime for which the exponent of 2 is also a Mersenne?

Perhaps that is a good project for the next Century when every home will have a Supercomputer......

[Ernest_at_the_Beach]

OK....let's try this :

Marin Mersenne

Supports Rightwhale's comment on Mersenne and gives further detail on the Mersenne Prime's.....

******************************************************

Mersenne's name is best remembered today for Mersenne primes.. He tried to find a formula that would represent all primes but, although he failed in this, his work on numbers of the form

2^p - 1, p prime

has been of continuing interest in the investigation of large primes. It is easy to prove that if the number n = 2^p - 1 is prime then p must be a prime. In 1644 Mersenne claimed that n is prime if p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 but composite for the other 44 primes p smaller than 257.

Over the years it has been found that Mersenne was wrong about 5 of the primes of the form 2^p - 1 where p is less than or equal to 257 (he claimed two that didn't lead to a prime (67 and 257) and missed 3 that did: 61, 89, 107). Drake [13] has tried to both understand the source of Mersenne's work on these primes, and also to try to determine the rule that was being used. He suggests Frenicle de Bessy may be the source and also suggests that the errors might be misprints by the printer. Drake reconstructs Mersenne's rule for exponents as that they must differ by not more than one from a value of 2ⁿ or by not more than three from a value of 2 to the power 2ⁿ.

[Lonesome in Massachussets]

2^127 - 1 ??

[Lurker]

Alright I get it.

But this begs the next question. What do you do with them once you find them?

Other than redeem them for valuable prizes I mean.

L

[Ernest_at_the_Beach]

Another reference:

Mersenne Primes:
History, Theorems and Lists

and at Section 5...we have

5. Conjectures and Unsolved Problems

[Ernest_at_the_Beach]

There is a pot of money .....

the prime was confirmed and it is 9,152,052 digits long, which means that the $100,000 EFF prize for the first 10 million digit prime is still up for grabs.
I'd speculate that the next Mersenne prime will probably be over 10 million digits, so if you're a prize money DCer, now would probably be the time to get involved. ;)

[Ernest_at_the_Beach]

A break from Politics....

[Ernest_at_the_Beach]

fyi