ElevenSmooth
M(3326400) = 23326400-1
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ElevenSmooth
M(3326400) = 23326400-1 |
ElevenSmooth is a distributed computing project searching for prime factors of M(3326400) ...(more)
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May 1, 2009: yoyo@home user [ESL Brigade] NaiV found a P43 that reduced the unfactored primitive of 26160+1 from C1142 to C1099. This is the second known factor of this primitive; the other known factor is a P15 also found by ElevenSmooth.
Apr 13, 2009: yoyo@home users found a P48 and a P50 for 23080+1, finishing the factorization of this primitive by leaving a P481. User jalmari found the P48 at 9:40 CET on Easter Sunday, then user Bent Vangli finished the number with a P50 at 12:20. No factors were previously known for this primitive. The factors were all confirmed prime with Dario Alpern's Java factoring applet. This is the sixteenth primitive for which ElevenSmooth has completed the factorization, and the fourth done by yoyo@home.
Mar 30, 2009: yoyo@home has completely factored a second primitive in three days. User Marc1 found a P49 from 23780+1 leaving a P457 which completes the factorization of this primitive; the only other factors are a P7 and a P9 that were known before the founding of ElevenSmooth. The factors were confirmed prime with Dario Alpern's Java factoring applet. This is the fifteenth primitive for which ElevenSmooth has completed the factorization.
Mar 27, 2009: yoyo@home user Aflatoxin found a P51 from 23360+1 leaving a P393 which completes the factorization of this primitive; a P8 and a P13 were known before the founding of ElevenSmooth. This is the largest factor ElevenSmooth has found by ECM, and this is the fourteenth primitive for which ElevenSmooth has completed the factorization.
Mar 22, 2009: yoyo@home user [TEMPLAR] Kaar found a P49 from 23465-1. This is the third known factor of this primitive; a P7 and a P14 were known before the founding of ElevenSmooth. The composite cofactor is reduced from C414 to C365. This is the second largest factor ElevenSmooth has found by ECM, and largest factor by any method (except prime cofactor) in 10 months.
Feb 19, 2009: yoyo@home user blitzen found a P44 from the Aurifeuillian-M of 24158+1. The Math FAQ pages explain Aurifeuillian factors; this one is 22079+21040+1. This is the second known factor of this primitive; a P21 was previously found by ElevenSmooth. The composite cofactor is reduced from C305 to C262.
Feb 14, 2009: yoyo@home user Stefan Ver3 found a P37 from 215120+1 on Valentine's day. Yoyo's mission is to bridge existing distributed computing projects into the Boinc world. ECM is his most recent project, and ElevenSmooth is one of the participating projects. Two small factors were previously known; this reduces the composite cofactor from C2063 to C2026.
Jan 23, 2009: Rocke Verser continues to work the "soft side" of ElevenSmooth and has found another factor, this time a P37 from M(100800). This is the second known factor of this primitive, both found by ElevenSmooth. The composite cofactor has been reduced from C6925 to C6889. I've been slow to update the site; Rocke found this factor on Nov 15.
The "soft side" of ElevenSmooth has the factors of 21663200+1. Most of these primitives are not yet in the ECM Server. They received effort as part of the "Special Project" that used Prime95 on the entire 23326400-1. Rocke is the lastest of several searchers that have looked at this side in personal searches. Thanks, Rocke.
July 16, 2008: Rocke Verser has found a fifth ElevenSmooth factor! This P34 from M(5400) was found with ECM at the B1=1M level. This reduces the unfactored residual from C406 to C373. This is the second factor ElevenSmooth has found for this number.
July 6, 2008: Rocke Verser has found factors of three ElevenSmooth composites with ECM. The C217 from the M-Aurifeuillian of M(6300) cracked as P29 * P179 on June 11th. Then the C1266 from the L-Aurifeuillian of M(41580) yielded a P43 on July 4th and the C312 from the L-Aurifeuillian of M(7700) yielded a P31 on July 6th. In 1997 Rocke wrote the DESCHALL client program that solved the original RSA DES Challenge, using distributed computing and brute force to break 56 bit encryption.
The ElevenSmooth Project had previously found two factors for each of M(41580) and M(7700).
The factorizations are now
M(6300) M-part = P39 * P179
M(7700) L-part = P5 * P10 * P18 * P20 * P31 * C282
M(41580) L-part = P15 * P22 * P43 * C1223
May 7, 2008: Tom Womack's team effort has completed factoring M(2376). This C195 has been the smallest ElevenSmooth composite since March 8th, when Tom finished the previous ElevenSmooth factorization. The team sieved for two months, coordinating on this thread.
The factorization announcement tells us "it took two hours on one C2/2400 CPU to build a 7933391 x 7933638 matrix with weight 536309417, about 180 hours on four C2/2400 CPUs to find 49 dependencies, and about 2:45 per dependency for the square roots; success came on the second dependency." The primitive part of 21188+1 is now fully factored as P6 * P17 * P57 * P138. The previously known P17 factor was found by Bob Silverman in January 1986 and is Cunningham factor #1600.
Thank you to Tom and rest of the team!
March 8, 2008: Tom Womack has completed factoring the smallest ElevenSmooth composite and is leading a group to factor the next smallest. The smallest, a C149 from M(1575), factored as P69 * P80. The complete factorization of the primitive part of M(1575) has 6 primes. A P33 factor was found by ElevenSmooth in 2003. A P8, P11, and P17 were known prior the founding of ElevenSmooth. Full details of Tom's GNFS factorization are available at the ElevenSmooth Forum.
Tom is active in the factoring community. He has led team project for NFS factoring and often provides mathematical help on the Mersenne Forum boards. He completed a PhD in Number Theory in 2003 and now works as a computational chemist. His wide ranging interests include travel, singing, and photography. For more information visit his slightly outdated home page.
Sieving in progressing to finish the C195 from M(2788). You can participate by reserving a range in the thread.
January 15, 2008: Pierre Jammes has found his second ElevenSmooth factor, a P47 factor of M(5040). Pierre is a post-doc in mathematics at the University of Avignon researching riemannian geometry. Factorization projects are his hobby - in addition to ElevenSmooth, he is a regular contributor to the homogenous Cunningham project and the xy+yx project.
This is the second known factor of the primitive part of 22520+1. The other known factor, a P23, was also found by the ElevenSmooth project. This factor reduced the unfactored composite from C324 to C278. Coming early in the year, the factor was briefly on Paul Zimmermann's list of the 10 largest ECM factors so far in 2008.
May, 22 2007: We have found eight factors since the last update, and have completed the factorization of two more primitives. Six of those factors, and both primitives, came in a two day flurry last November. (Yes, I've been negligent about updates).
Jay Berg found five of the factors using his program to automate the Stage 1-2 process of using Prime95 and GMP-ECM. He completed M(1925) by finding a P32 which left a P248 cofactor; he also found a factor of each of M(4400), M(8800), and M(9900). Jay struck paydirt by using this tool to search the half of ElevenSmooth's factor-space that is not in the ECM Server, previously searched only in the "Special Projects" using Prime95 to do combined ECM on all algebraic factors. About himself Jay says "I hammer on numbers because I enjoy doing so …"
Pierre Jammes is at the University of Avignon in France, and has been a stalwart worker on the ECM Servers. He found a 46 digit factor of M(4032) which left a P263 cofactor.
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, 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 has been updated to show the factor.
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. 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 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 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 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.
July 28, 2005: As factors get scarce, interest in ElevenSmooth has declined. But loyal members have continued on, and that effort has been rewarded by the discovery of a new factor.
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.
October 19, 2004: Alan Lawrence has found his second ElevenSmooth factor one month after his first! Back to back factors by the same person has only happened twice before outside of the Special Project. This time Alan found a P36 factor of M(11880), the second known factor for the primitive part of this number. This reduces the unfactored composite from C853 to C818. Maybe we should rent a Frank Lloyd Wright house from Alan and ply him with Bass Ale to learn his secrets for finding factors.
September 18, 2004: Alan Lawrence of Sand County Service Company found a P28 factor of M(95040). For your next vacation rent a Frank Lloyd Wright house in the scenic Wisconsin Dells and visit with Alan. This is the first known factor of the primitive part of M(95040). The 6936 digit composite was tied for the largest number under active search at ElevenSmooth. The remaining 6909 digit composite is now the second largest number under active work.
July 20, 2004: Today Thomas Lipp completed the factorization of the Mersenne number M(3960) by splitting the remaining 198 digit composite into two primes of 47 and 151 digits. The P47 is the second largest factor ever found by ElevenSmooth using ECM; the remaining P151 is our sixth largest factor by any method. This is our eighth completed Mersenne factorization. We had previously found a 37 digit factor for this number.
Thomas was using the Prep Server on port 8196. This server prepares numbers that are not yet ready for the Record Server on port 8195. Thus it is disappointing but not surprising that this factor is two digits too small to be listed on Paul Zimmermann's Top 10 This Year or Top 50 All Time pages.
June 12, 2004: Over three days Dennis Kelly found a 25 digit factor and Mark Rodenkirch found a 49 digit factor. The P49 is large enough to be listed, for a while, on Paul Zimmermann's Top 10 This Year page, where it will debut in the eighth position. This is the largest factor ever found by ElevenSmooth using ECM.
Dennis Kelly's P25, found on June 9th, is only the second known factor of the primitive part of M(66528). The other factor was also found by ElevenSmooth. This was an elusive factor; we had finished the search stage for 25 digit factors and were over 10% of the way through the search stage for 30 digit factors. This is expected to happen from time to time because of the probabilistic nature of ECM factoring. The unfactored composite was reduced from C5184 to C5159.
Mark Rodenkirch was one of earliest members of ElevenSmooth, and also one of the unluckiest. In the early days many people found small factors with small effort, but Mark tested on and on without results. But when he finally found a factor on June 11th, what a factor it was! It's nearly 20% longer than the previous ElevenSmooth record for ECM factors. Mark found this using the Record Server on port 8195, where factors are scarcer but likely to be listable. This is third known factor for the primitive part of M(1485), the second one found by ElevenSmooth. The C184 was the second smallest composite in the ElevenSmooth project; the remaining C135 is the smallest composite.
It was a surprise that we were competitive for so long; I had expected the cutoff to outrun our ability in January. However, a short term boost of about twenty machines was enough to keep us in the running for much longer. We didn't have much luck actually finding factors though - we found two factors that each stayed on the list for less than a week.
The standard server, on port 8194, will return to using mostly the allocation method of Sum-of-B1 times Length Squared, with a small amount of Random and tiny bit of Smallest Composite. Ports 8195 and 8196 will be a mix of Record Sized Factors and Preparation for Records. Port 8200 is presently in an experiment of sharing ElevenSmooth numbers and Cunningham numbers.
To further increase this pool, I’ve been concentrating on numbers that are almost finished testing at the 35 digit level. Today I also adjusted the public ecm server to this task. It looks like we will have more than a dozen additional numbers ready by January. This will make at least three dozen numbers suitable for the list, with many numbers nearly untested at 40 digits.
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M( 4032 )C: 967287298662167339558077202115073 M( 3520 )C: 876842301273103818127810927797272474881 M( 3520 )D M( 14784 )C: 507649231049494939716780475777 |
Will Edgington has been informed and the remain 714 digit composite is now in the ecm servers.