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Розподілені обчислення в Україні _ Математика (завершені проекти) _ ElevenSmooth

Автор: nikelong Feb 9 2009, 20:57

ElevenSmooth
http://home.earthlink.net/~elevensmooth/

http://www.rechenkraft.net/wiki/index.php?title=ElevenSmooth

Автор: Death Feb 10 2009, 11:43

Ищут неизвестные ранее простые делители для числа 2^3,326,400-1.

ElevenSmooth is a http://www.aspenleaf.com/distributed/ searching for prime factors of M(3326400).

http://mathworld.wolfram.com/MersenneNumber.html numbers of the form 2n-1, are named for the French mathematician

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mersenne.html (1588-1648).

Prime factors of Mersenne numbers are occasionally useful to mathematicians.
For example, http://NFSNET.org/ factored M(713)=2^713-1 to help in Richard Brent and Paul Zimmerman's
http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pd/rpb212.pdf
Primitive trinomials have applications in cryptography, coding theory, and random number generation.

Factors of Mersenne numbers are also central to the study of http://www.glasgowg43.freeserve.co.uk/siercvr.htm for http://www.prothsearch.net/sierp.html, http://www.prothsearch.net/rieselprob.html, and http://www.glasgowg43.freeserve.co.uk/brier2.htm numbers.

The http://www.cerias.purdue.edu/homes/ssw/cun/ has been collecting Mersenne factors (and other factors) since 1925.

There is enough interest in Mersenne factors that Will Edgington updates the file of known factors every few weeks on http://www.garlic.com/~wedgingt/mersenne.html.

Автор: nikelong Mar 9 2009, 14:06

Find factors of the Mersenne number M(3326400) = 23326400 - 1 in ElevenSmooth. Note: this project is active, but the project website is not updated unless a major event occurs. The website was last updated on February 19, 2009.

On February 1, 2004 the project "found a 42 digit factor of M(5280) using GMP-ECM with B=3M. This is expected to qualify for 9th place in Paul Zimmerman's http://www.loria.fr/~zimmerma/records/ecmnet.html#top10." On April 4, 2004, the project found P35, the first known primitive factor of M(15840). On May 14, 2004, the project found P34, the second known factor of M(10395). On June 9, 2004, the project found P25, the second known factor of the primitive part of M(66528). On June 12, 2004, the project found a P49 factor for M(1485), the largest factor found by ElevenSmooth using ECM. On July 20, 2004, the project completed the factorization of M(3960). On September 18, 2004, the project found a P28 factor of M(95040): this is the first known factor of the primitive part of M(95040). On October 19, 2004, the project found a P36 factor of M(11880), "the second known factor for the primitive part of this number." On July 28, 2005, the project found a P35 factor of M(47520), the third factor the project has found for the primitive part of M(47520). In early December, 2005. the project found a 41-digit factor of M(6336). In March, 2008, the project completed the factorization of M(1575). On May 7, 2008, the project completed the factorization of M(2376). On July 16, 2008, the project found a P34 factor of M(5400) (using ECM at the B1=1M level). This factor reduces the unfactored residual from C406 to C373. This is the second factor ElevenSmooth has found for this number. On November 15, 2008, the project found a P37 factor of M(100800). This factor reduces the unfactored residual from C6925 to C6889. See news of more recent factor discoveries on the project's main page.

To participate in the project, http://www.elevensmooth.com/ElevenDown.htmlthe ECMclient application and configure it according to the directions on the download page (if you already have the ECM or ECMclient application installed, you only need to reconfigure it to use server=wblipp.dynu.com and port=8194). Unix users can http://www.ecompute.org/factors/unix.htmlinstructions to create an ECM client for Unix. Once ECMclient is configured, it contacts the ElevenSmooth project server to get work units and to return results. It processes a work unit for 30 minutes by default, but you can change the processing time by changing the maxfreq parameter. The project supports users behind firewalls and possibly proxy servers. It supports modem users with a little bit of work. See the help page for http://home.earthlink.net/~elevensmooth/ElevenHelp.htmlabout using firewalls, proxy servers, and modems.

The project also has a http://www.elevensmooth.com/ElevenFAQ.html#Special for users who have contributed at least one full week to the main ECM project. The Special Project "uses GIMPS' program Prime95 to work on all primitives of M(3326400) simultaneously. If any ECM work is going to be done on the largest composites, Prime95 is much faster. The subfactor composites are then tested 'for free.' However, even with Prime95, it takes a long time to run ECM curves on large numbers." Users who qualify for this project will be invited by email to join it.

See the project's http://home.earthlink.net/~elevensmooth/Progress.htmland http://home.earthlink.net/~elevensmooth/Progress.html#completefactorizations.

Join a http://www.mersenneforum.org/forumdisplay.php?s=&forumid=31 about the project.