Elevensmooth Project News

News and project updates which haven't been added to distributedcomputing.info yet.

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Elevensmooth Project News

Postby Jwb52z » Wed Nov 16, 2005 7:01 am

News
Leyland and Hoogendoorn GNFS the C135 —Finishes M(1485), M(2970), & M(5940)
November 14, 2005: Paul Leyland and Sander Hoogendoorn teamed up to factor the smallest ElevenSmooth composite, a C135 from M(1485), into P61 x P75. The factors are on the factors page,http://home.earthlink.net/~elevensmooth/ElevenFactors.html . They used the General Number Field Sieve, sharing the polynomial search and sieving with Paul doing the post processing. Additional information is available on the forum thread, http://www.mersenneforum.org/showthread.php?t=4855 , where they originated and coordinated this project.

ElevenSmooth had previously found two factors for this Mersenne number. These factors complete the factorization of M(1485). M(1485) is an algebraic factor, http://home.earthlink.net/~elevensmooth ... #Algebraic , of M(2970) and M(5940). Thanks to three other factors previously found by ElevenSmooth, their factorizations are now complete, too.

Congratulations to Sander and Paul!

Karli finds another P35
Karli Lopez has found a P35 factor of M(47520). This is the second ElevenSmooth factor for Karli; the other was a 35 digit factor of M(15840). This is the third factor that ElevenSmooth has found for the primitive part of M(47520). The remaining unfactored C3386 continues in the ECM Server.
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Postby Jwb52z » Wed Nov 16, 2005 8:11 pm

According to this thread: http://www.mersenneforum.org/showthread.php?t=4855 there are errors in the latest page update, but they haven't been changed on the main page from which I copied the information. This URL lists the few errors there are now.
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Postby Jwb52z » Tue Dec 27, 2005 8:55 am

Greg Childers finds Record P+1 Factor after ECM Server Upgrade
December, 2005: The ElevenSmooth server was upgraded to version 2.6.3 at the end of November. This version handles P-1 and P+1 as well as ECM. This paid off a few days later when Greg Childers found a 41 digit factor of M(6336) by P+1. This was a remarkable example of the extra factors sometimes found with the polynomial extensions. The largest factor of P+1 is 7.8 x 10^22, but the 41 digit divisor was found using the default B2 value of 2.2 x 10^9.

Only the tiny factor 63361 was previously known for the primitive part of 2^3168+1. This factor reduces the unfactored part from C574 to C534. The factors page has been updated to show the factor.

Note: There is a little quibble right now over this news from some of the more math knowledgeable on the Mersenne forum. If or when there needs to be an update or change because of what they decide, I will post it here.
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Postby Jwb52z » Tue Dec 27, 2005 11:34 pm

As promised, here are the required changes:

Greg Childers finds P41 Factor after ECM Server Upgrade
December, 2005: The ElevenSmooth server was upgraded to version 2.6.3 at the end of November. This version handles P-1 and P+1 as well as ECM. This paid off a few days later when Greg Childers found a 41 digit factor of M(6336). The factor was found when requesting the P+1 method, but many P+1 attempts actually result in P-1 calculations. As explained at MersenneWiki, http://www.mersennewiki.org/index.php/P ... ion_Method , this happens because the correct starting values for P+1 cannot be determined until after the prime P is known. This factor is one of the extra factors sometimes found through the polynomial extensions. GMP uses different polynomials for P+1 and P-1, so we have the surprising situation that this P-1 factor is found only when attempting a P+1 factorization (at B1=11M).

Only the tiny factor 63361 was previously known for the primitive part of 23168+1. This factor reduces the unfactored part from C574 to C534. The factors page, http://home.earthlink.net/~elevensmooth ... ctors.html , has been updated to show the factor.
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Postby Jwb52z » Thu Dec 29, 2005 12:20 am

Another new factor has been found: http://www.mersenneforum.org/showthread.php?t=5220
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Postby CedricVonck » Sat Dec 31, 2005 7:25 pm

On the other hand, I cannot reach the ecmnet of ElevenSmooth anymore...
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Postby Jwb52z » Mon Jan 02, 2006 6:28 am

Apparently that new factor found in: http://www.mersenneforum.org/showthread.php?t=5220 , has something to do with Oddperfect.org's project too.
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