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Math Science

47th Mersenne Prime Confirmed 89

radiot88 writes to let us know that he heard a confirmation of the discovery of the 47th known Mersenne Prime on NPR's Science Friday (audio here). The new prime, 2^42,643,801 - 1, is actually smaller than the one discovered previously. It was "found by Odd Magnar Strindmo from Melhus, Norway. This prime is the second largest known prime number, a 'mere' 141,125 digits smaller than the Mersenne prime found last August. Odd is an IT professional whose computers have been working with GIMPS since 1996 testing over 1,400 candidates. This calculation took 29 days on a 3.0 GHz Intel Core2 processor. The prime was independently verified June 12th by Tony Reix of Bull SAS in Grenoble, France..."
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47th Mersenne Prime Confirmed

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  • Re:Cool processor (Score:5, Informative)

    by Jarlsberg ( 643324 ) on Saturday June 13, 2009 @07:05PM (#28323151) Journal
    It was found through the GIMPS (The Great Internet Mersenne Prime Search). The site http://www.mersenne.org/prime.htm [mersenne.org] is currently down.
  • Re:Cool processor (Score:4, Informative)

    by Kurusuki ( 1049294 ) on Saturday June 13, 2009 @07:08PM (#28323161)

    They're crunching 13-million-digit numbers with a desktop processor? Do they realize that they can put eight quad-core xeons in a machine and finish the calculation in a single shift instead of waiting a month?

    I don't know about you, but the last 13 or so mersenne primes have been found using prime95 as a conduit for a mass distributed effort. I'm not sure where you live, but in most other places people can't just go out and put 8 quad-core xeons in a home machine.

  • Re:Cool processor (Score:5, Informative)

    by JoshuaZ ( 1134087 ) on Saturday June 13, 2009 @07:19PM (#28323231) Homepage

    The system used for this is GIMPS, the Great Internet Mersenne Prime Search. The system uses a distributed computing system using unused computing power in personal computers to search for various candidate primes. Computers do one of two things: Either trying to factor candidate Mersenne numbers or running a Lucas-Lehmer test on candidates without any small prime factors (the Lucas-Lehmer test is a special primality test for Mersenne numbers that is very fast). They use modular arithmetic and a variant of the Fast Fourier Transform to handle the multiplications which might otherwise become too difficult. The procedure is naturally a problem that can be made into a parallel processing problem like this since there are so many different candidate numbers to look at.

    The summary doesn't mention but it is worth noting that the Lucas-Lehmer test allows one to check the primality of Mersenne numbers (numbers of the form 2^p-1, p prime) much faster than you can test the primality of generic numbers (or almost any other specialized form). Thus, for most of the last hundred years the largest primes known have been Mersenne primes. Currently the largest known prime is a Mersenne prime and the next 4 largest are also Mersenne primes. The GIMPS website - http://mersenne.org/ [mersenne.org] has a lot more details of both the math and software and explains how you can join in to help the project.

  • Hmm (Score:4, Informative)

    by Anenome ( 1250374 ) on Saturday June 13, 2009 @07:36PM (#28323335)

    I honestly forget why I'm supposed to care about Mersenne primes. Like, I read something about them awhile back, it was somewhat interesting... and then--yeah. So:

    http://en.wikipedia.org/wiki/Mersenne_prime [wikipedia.org]
    In mathematics, a Mersenne number is a positive integer that is one less than a power of two.

    A Mersenne prime is a Mersenne number that is prime. As of June 2009[ref], only 47 Mersenne primes are known; the largest known prime number (243,112,609 1) is a Mersenne prime, and in modern times, the largest known prime has almost always been a Mersenne prime.[1] Like several previously-discovered Mersenne primes, it was discovered by a distributed computing project on the Internet, known as the Great Internet Mersenne Prime Search (GIMPS). It was the first known prime number with more than 10 million base-10 digits.

    For those who can't even remember what a prime is, it's a number that can only be divided (evenly) by 1 and itself. Here's a list of the first primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

    The Mersenne primes are the largest known primes.

    Prime numbers have applications in electronic security and encryption breaking. I'm not sure what other purpose there is to knowing them, other than knowing them. The Mersenne in particular seem to be merely mathematical curiosities right now.

    I was much more excited by the discovery that the the Fibonnacci sequence is contained within the 1/89 calculation.
    http://www.geom.uiuc.edu/~rminer/1over89/ [uiuc.edu]

  • by JoshuaZ ( 1134087 ) on Saturday June 13, 2009 @08:03PM (#28323485) Homepage
    The historical reasons for caring about Mersenne Prime are twofold: First, Mersenne primes correspond to perfect numbers (numbers that are the sum of their positive less than the number. So for example, 6 has as proper divisors 1,2 and 3 and 1+2+3=6). The ancient Greeks were fascinated by perfect numbers but could not do much to understand them. Euclid showed that if one had a Mersenne prime one can construct an even perfect number. In particular, if 2^n-1 is prime then (2^n-1)*2^(n-1) is perfect. Almost 2000 years later, Euler showed that every even perfect number is of Euclid's form. Thus, investigating Mersenne primes tells us more about perfect numbers. The oldest unsolved problems in math are 1) are there any odd perfect numbers? and 2) are there infinitely many even perfect numbers? Thus, investigating Mersenne primes helps us get closer to solving one of the two oldest unsolved problems in mathematics.
  • by davmoo ( 63521 ) on Saturday June 13, 2009 @08:47PM (#28323725)

    Do they realize that they can put eight quad-core xeons in a machine and finish the calculation in a single shift instead of waiting a month?

    No, they can't. Each iteration of the software requires the results of the previous iteration. It cannot easily be made to run like you want on multiple cores. The best they could do on the processor you describe is run 8 separate copies of the application, each taking one month to run...they could test 8 numbers at once, but they cannot test one number 8 times as fast.

  • by rbarreira ( 836272 ) on Saturday June 13, 2009 @09:05PM (#28323801) Homepage

    Actually that's not exactly correct, each iteration is also parallelizable. Most of the work in an iteration is a FFT, which is parallelizable.

    http://www.fftw.org/parallel/parallel-fftw.html [fftw.org]

    It's less efficient to do this than using each core for one independent number, so it's only used if quick checking of a number is desired (for example, when double-checking a previously found prime number).

  • Re:Cool processor (Score:3, Informative)

    by Daswolfen ( 1277224 ) on Saturday June 13, 2009 @11:52PM (#28324461)

    As one of the IT guys who maintain the lab that found the 43rd and 44th primes at University of Central Missouri (formerly CMSU), I can tell you its one number per core. Also, these are production machines in computer labs as well as classroom, faculty and staff systems that run the GIMPS software.

    We are a public university, its not like we have extra $5k machines just sitting around crunching a number. BTW, the systems that found the 43rd and 44th prime numbers were base model Dell GX280s.

  • by smallfries ( 601545 ) on Sunday June 14, 2009 @06:40AM (#28325649) Homepage

    If you were going to test for primality by sieving then you could take a process that is millions of times slower than the primality test used, and speed it up by a factor of 8.

    Instead the test being discussed performs a series of squares and modulo reductions. Each operand is dependent on the previous result - the entire computation is one long dependency chain and so cannot be split onto multiple cores in the way that you describe.

    Although having said that, it all flips around again if you look inside the primitive operations that the primality tests uses. So they're using FFT based multiplication steps to do the squaring which obviously can be parallelised quite well..

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