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47th Mersenne Prime Confirmed
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..."
It was found through the GIMPS (The Great Internet Mersenne Prime Search). The site http://www.mersenne.org/prime.htm is currently down.
So, all primes greater than two are odd, but only one of them is Odd's!
My first program:
Hell Segmentation fault
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.
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?
What makes you think they aren't?
And what makes you think this man would pony up the serious coin for such a beast just to find a prime number?
"I don't know, therefore Aliens" Wafflebox1
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/ has a lot more details of both the math and software and explains how you can join in to help the project.
I'm not sure where you live
He lives at home with his parents (or maybe in a dormitory room) and doesn't have a clue as to what it actually costs to run a home.
"I don't know, therefore Aliens" Wafflebox1
The admins missed the prime for about a month
http://mersenneforum.org/showthread.php?t=11996
Apparently the email that was supposed to be sent wasn't when the prime was reported
The Singularity is closer than you think
Quant
Discovering a prime number that distant from the zero is like discovering a Pluto like planet in outer space. But instead of Hubble telescope you need a powerful mathematical one..
What are the odds this odd odd would be found by Odd?
http://ifrolf.com/
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
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/
"I Don't Have Enough Faith to be an Atheist"
The answer is not in the summary, nor in the first page of the FA...
Buried somewhere in the linked site is this FAQ:
http://primes.utm.edu/notes/faq/why.html
However all the answers are a bit unsatisfactory, IMHO...
So, I ask the great Slashdot hive-mind... What are the practical applications of Mersenne Primes and why are people paying money to find them?
No sig for the moment.
Do you realize that that's less efficient than using those 32 cores to calculate 32 independent numbers?
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
My calculator doesn't show it, anyone have the value of the prime?
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.
Well I don't know why it took 29 days for the computer to tell him it was so, wolfram alpha told me it was prime in ~1 second.
On that note, I asked Wolfram the other day the tree in a forest thing and I finally have an answer!
like phosphorescent desert buttons singing one familiar song
*hands you the key to the city*
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.
I want a new quote. One that won't spill. One that don't cost too much. Or come in a pill.
My bad...I misread your processor description...I thought you said 8-core. My answer is still correct though, I just used the wrong number of copies. They can run one copy per core, and the copies cannot exchange information.
I want a new quote. One that won't spill. One that don't cost too much. Or come in a pill.
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
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).
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
... the Great Old Ones will return, all life on earth will be destroyed.
weinersmith
You mean especially since the bounty for a prime goes from $100K - $250K?
A loop, by its nature, continues. If that didn't make sense, start reading this sentence again.
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.
Don't rush me, Sonny. You rush a miracle man, you get rotten miracles.
Quite oddly high, it seems... I guess it's not so odd anymore that he is an accomplished oddity...
Previously: "Linux... Toward the Sunrise..." Now: "Linux... Toward the-- No, now, part of Every Sunrise"
You don't get the $100k by searching for one prime though. You've got to be the lucky one that does the month long calculation on the number that actually happens to be prime.
It's like the lottery. You can't make a profit at it unless you're lucky. Otherwise, some big company would come in, invest a few million in number crunching, and take home all the bounties.
According to the The Hitchhiker's Guide to the Galaxy, "Odd Magnar Strindmo" was a fourth generation accounting prefect on the third major planet of the second solar system in the first minor galactic cluster directly to the "left" of the vicinity of Betelgeuse - a star that has recently gone supernova. After achieving a modicum of fame for discovering the 47th known Mersenne Prime, during extended holiday on the, mostly harmless, planet named Earth, Mr Strindmo retired to a life of semi-luxury where he preferred to be called "Steve".
It must have been something you assimilated. . . .
"they could test 8 numbers at once, but they cannot test one number 8 times as fast."
Just because most searches use one number per core does not mean testing a single candidate can't be done very efficiently over multiple cores. You only have to think about the process for finding a prime, ie: testing factors, test if the candidate is it divisable by two, three, five, ect. The test for each factor is independent, so you COULD test 8 factors simultaneously, no?
The only communication between threads is a semaphore to say "stop, thread XYZ found an integer factor", if you want to be pedantic it's not 8X as fast but rather close to 8X as fast. I suggest the reason most implementations use one candidate per core is because most searches look at more than one candidate and the semaphore test makes the alternative implementation slightly less efficent.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
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..
Slashdot: where don knuth is an idiot because he cant grasp the awesome power of php
"Instead the test being discussed performs a series of squares and modulo reductions."
:)
Thanks for showing an old dog a new trick.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
The primality test for these Mersenne primes does not consist of sieving, that would be way too slow given the size of these numbers.
Instead, the Lucas-Lehmer test is used, a very simple iterative process which you can implement in a few lines of code in most programming languages. It's described here:
http://primes.utm.edu/mersenne/index.html#test
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
I say the entire number was photoshopped.
It's disappointing that they're using a home-grown management software instead of BOINC like many of the other distributed computing projects. I, for one, would be much more likely to add to the effort if I didn't have to worry about another piece of software and how it shared resources with the Einstein and Rosetta I'm already running.
My life's goal is to get a score of +3!
They're about even.
xkcd is not in the sudoers file. This incident will be reported.
crypto man, crypto.....
"It's the Law of the Universe, and I'm the sheriff." Slash-cott 2/10-2/17
I'm not referring to Odd Magnar Strindmo.
"I don't know, therefore Aliens" Wafflebox1
The dashed form of the English name is available at assist those who might actually want to read all or part of the +324 Megabyte name. :-)
chongo (was here)
I'm surprised that your 280s could take it. We have a load of those here and the PSUs are all starting to flake out. Even before that, the 280(desktop and SFF models anyway) is not what I'd call well ventilated.
These are all the tower models, which have better air flow. The problem is that systems of that era are subject to the burst capacitors (look for the ones with an X rather than a K or T) and we did have issues with that as well, but we preemptively replaced MBs and PSUs of the of the ones with failing capacitors before our warranty ran out.
As far as running the software, GIMPS is usually pretty good about sharing processor time, and some of the heavier use labs are scheduled to run 9pm-7am.
The nice part is we can crank out a lot of numbers when you have 500+ systems all running GIMPS in the background :)
Don't rush me, Sonny. You rush a miracle man, you get rotten miracles.