Re: [math-fun] New Mersenne Prime
[ I think 'Mersenne Primes' is why I'm on the maths-fun list. Thanks Richard. ] The record M(57,885,161), discovered by Prof. Cooper et al, is a prime with 17,425,170 decimal digits. It is the 48th known prime M(p). It may yet not be the 48th in size: GIMPS have only just confirmed the '42nd by size' position of the prime M(p) discovered in 2005. http://www.mersenne.org/report_milestones/ Its discovery ends the longest wait - nearly 4 years - for the 'largest prime' record to be broken since the Great Internet Mersenne Prime Search (GIMPS) began. Curt Noll kindly credited my Mersenne work 30 years ago as being part of the reason GIMPS began, hence Chris Caldwell's note at http://primes.utm.edu/glossary/xpage/GIMPS.html Dan Shanks, whose wonderful book first interested me in Mersenne Numbers in 1967, included an amusing piece about that work in the 3rd edition. GIMPS is the oldest continuously running crowd-sourced programme running on the web and has clocked over 100 TFLOPS. The prime-indexes, circa 100,000, that my ICL colleagues were working with then seem so small now! The back-history to 1987, and our modest results of the 1980s, can be consulted here: Back-history: http://centaur.reading.ac.uk/4571/1/1987_H_Mersenne_Numbers.pdf ICL DAP results: http://centaur.reading.ac.uk/5948/1/1986_H_Mp_Consolidated_Results.pdf AMS Abstracts note 1: http://centaur.reading.ac.uk/4555/1/1983_Abstracts_of_the_AMS_v4.2_p196.pdf AMS Abstracts note 2: http://centaur.reading.ac.uk/4572/1/1986_Abstracts_of_the_AMS_v7.2_pp224-5.p... Huge congratulations to Prof. Cooper and team. It is the third prime M(p) that they have found. M(M(31)) remains the largest Double Mersenne Number whose primality status is known and that record may stand for 31 years (1983-2014) ... see 'Back History' above ... :-) Guy
On Wed, Feb 6, 2013 at 3:24 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
The record M(57,885,161), discovered by Prof. Cooper et al, is a prime with 17,425,170 decimal digits. It is the 48th known prime M(p).
It may yet not be the 48th in size: GIMPS have only just confirmed the '42nd by size' position of the prime M(p) discovered in 2005. http://www.mersenne.org/report_milestones/
What are the reasons that the prime M(57,885,161) was discovered before verifying what the `43rd by size` is? Is it just that nobody wants to find a prime smaller than the largest known prime?
It's a distributed project, so some computers finish faster than others. But more particularly, primes are not verified as being the n-th Mersenne prime until at least two computers have checked every exponent below that range to verify that (1) it has a known factor, (2) it is prime, or (3) it is composite. In the (likely) last case, the double check is not considered complete unless the residues match (to guard against machine errors). Charles Greathouse Analyst/Programmer Case Western Reserve University On Wed, Feb 6, 2013 at 2:08 PM, W. Edwin Clark <wclark@mail.usf.edu> wrote:
On Wed, Feb 6, 2013 at 3:24 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
The record M(57,885,161), discovered by Prof. Cooper et al, is a prime with 17,425,170 decimal digits. It is the 48th known prime M(p).
It may yet not be the 48th in size: GIMPS have only just confirmed the '42nd by size' position of the prime M(p) discovered in 2005. http://www.mersenne.org/report_milestones/
What are the reasons that the prime M(57,885,161) was discovered before verifying what the `43rd by size` is? Is it just that nobody wants to find a prime smaller than the largest known prime? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Hello everybody, I think the main reason is that : the test has to be conducted on 1 single CPU and it takes more than 2 months on 1 machine to test 1 exponent. Even if the project is distributed and has a cpu work force of 150000 machines, 1 test = 1 computer = several months. ... there are many prime numbers and as fas as I know there is no reason to think that one particular prime might be a candidate or not apart from some basic filtering techniques, like to take primes of the form 4n+1 or 4n+3, ... I know that since I tried that a long time ago, it does not really work. to test your own machine you may take a look at the following web page : http://www.mersenne.ca/cudalucas.php or here : http://www.mersenne.ca/bench.php beware : the page is huge in width. Best regards, Simon Plouffe
participants (4)
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Charles Greathouse -
Guy Haworth -
Simon Plouffe -
W. Edwin Clark