Searching for factors of the Mersenne number M(3326400) = 23326400-1

ElevenSmooth is a distributed computing project searching for prime factors of M(3326400) ...(more)

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Another Yoyo Cycle Completed

January 20, 2013: We have completed another cycle through our composites at yoyo@home. This cycle was to bring the newer composites closer to the work on the older composites and to even out the work vs size curve as seen in the Progress page. In addition to the previously reported factor, yoyo user Big.Benn found a P35 from 233264+1, leaving a C5096. Also RSALS, currently working as the 14e sub-project of NFS@home, did the GNFS to finish the C168 from 21584+1. Mathew did the post-processing. Another cycle of ECM has begun at yoyo@home with the same objectives.

P54 for 21584+1

November 8, 2012: yoyo@home user Shawn Reimerdes found a P54 that reduced the unfactored primitive of 21584+1 from C222 to C168. This is the fourth known factor of this primitive. A P33 was previously found by ElevenSmooth. The remaining composite has had sufficient ECM to justify GNFS factoring. It is the smallest ElevenSmooth composite, and is believed to be the sixth smallest Mersenne composite.


October 28, 2012: One new factor since the last update. Progress continues mostly on the new numbers. Some errors and broken links have been fixed.

March 16, 2012: I don't have much time for the ElevenSmooth project, but ECM is steadily advancing thanks to yoyo@home. I have updated the Factors page and the Progress page. We have found 16 ECM factors since the last update and finished three algebraic factors. The biggest change is that we are now working on many more of the algebraic factors. Previously most of the algebraic factors came from 21663200-1. I have extended the list to include factors from 21663200+1. Yoyo extended the size of numbers he can handle, so I also added some of the larger numbers. I'm currently bringing the added numbers into line with the ECM level of similar sized older numbers. You can watch this progress by the groupings on the Progress page.

P43 for 26160+1

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.

One-Two Punch Knocks Out 23080+1 on Easter

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.

Yoyo Completes Another Primitive

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.

Largest ECM yet, Yoyo's Fourth, Completes 14th Primitive

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.

Third yoyo-BOINC factor

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.

Second yoyo-BOINC factor

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.

BOINC Valentine

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.

Verser's Sixth

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.

Verser's Fifth

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.

Verser Finds Four Factors, Finishes 'Feuillian

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

Womack et al Finishes M(2376)

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!

Tom Womack Finishes M(1575), Leading Attack on M(2376)

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.

Pierre Jammes Strikes Again!

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.

Eight Factors Since Last Update

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.

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, 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.

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. 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 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.

Karli Finds Another P35

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.

Alan Scores Again!

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.

Alan Lawrence finds P28 in Wisconsin Dells

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.

Thomas Lipp Completes M(3960)

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.

Two New! P25 and a Record P49 for M(66528) and M(1485)

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.

More Beginners Luck factors M(10395)

May 14, 2004: Alexis Nunes started with two computers on May 11th and found a new prime factor on May 14th! Alexis' P34 is the second known factor of M(10395), both found by ElevenSmooth. This discovery reduced the unfactored primitive part from C1288 to C1255.

Karli Lopez finds P35 from M(15840)

Apr 4, 2004: The return to broad search paid off today, as Karli Lopez found a P35, the first known primitive factor of M(15840). Karli, a relative newcomer to ElevenSmooth, had a strong dose of beginners luck; I estimate the probability of finding a factor within his searches to have been only 7%.

Return to Broad Search

Mar 21, 2004: Today ElevenSmooth returned to a broad search strategy. When Paul Zimmermann's Top Ten This Year list opened in January, we started with 36 numbers that were searching for the list-minimum 40 digit factors. As the minimum advanced, our supply of suitable candidates dwindled, but a week ago we still had 22 viable candidates. However, a recent flurry of factors has advanced the threshold to the point where ElevenSmooth has only three suitable candidates.

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.

42 Digit Factor on Top Ten List

Feb 1, 2004: William found a 42 digit factor of M(5280) using GMP-ECM with B=3M. This is expected to qualify for 9th place in Paul Zimmermann's Top Ten This Year list. ElevenSmooth's previous entry on this last lasted only two days.

40 Digit Factor Debuts at Bottom of Top Ten List

Jan 25, 2004: Kimmo Herranen, Gipe on the boards, has found a 40 digit factor of M(5940) using GMP-ECM with B=11M. Paul Zimmerman's Top Ten This Year list already has 9 factors, beginning with 41 digits. This number will slip into the "bubble position", ready to be bumped by the next factor found.

Progress Page

Jan 22, 2004: A Progress Page has been added to the web site to report on progress of numbers in the ECM Server. It is directly linked from the bottom menu, and is linked under "Factors" in the upper right navigation box.

Record Search Begins

Jan 2, 2004: For January, all assignments from the ElevenSmooth ECM Server will be searching for factors of 40 or more digits. ElevenSmooth has three dozen such numbers, including a dozen that have not been previously searched at this level. All factors found are likely to qualify for inclusion in Paul Zimmerman’s list of the Top Ten Factors Found by GMP-ECM This Year, at least for a while.


Dec 17, 2003: Today our domain name became active. This page is now reachable as www.ElevenSmooth.com. The factors page can be reached as www.ElevenSmooth.com/ElevenFactors.html, and the download page can be reached as www.ElevenSmooth.com/ElevenDown.html.

Preparing for Records in January

Dec 16, 2003: I’m preparing for January, when Paul Zimmerman’s list of the Top Ten Factors Found by GMP-ECM This Year will reset. Forty digit factors will be sufficient to make the list, at least for a while. ElevenSmooth has twenty-three numbers testing in this range, so we have a rich pool of opportunity to make the list.

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.

New Server for Record Setting Factors at Port 8195

Nov 5, 2003: A slave ECM Server has been established that will only distribute assignments that are likely to qualify for the top 100 factors found by ECM or for the 10 largest factors found by GMP-ECM so far this year. At this time only the C149 composite from M(1575) qualifies - it is 80% finished testing at the 45 digit level (B1=11M) and will move to 50 digit level later this month. This server is at the same address (wblipp.dynu.com or elevensmooth.no-ip.com) on port 8195. To reach this server, change the "port" setting in the file ecmclient.cfg to 8195.

Infrastructure and Support

Oct 8, 2003: The ElevenSmooth web site is attracting help in many ways. The MersenneForum has given us our own Forum to discuss the project, and has given us the prestigous URL http://www.mersenneforum.org/elevensmooth. Aspenleaf found us and told the world about ElevenSmooth. Aspenleaf is probably responsible for an increase in ECM users over the weekend. I previously (Oct 2) reported the valuable programming assistance that Japke Rosink provided. Many people have provided questions and suggestions leading to extensive improvements of the web site. Andreas Pipp has agreed to be ElevenSmooth's Director of Publicity, and has listed us at the German distributed computing site Rechenkraft. I continue to be surprised and delighted at all the fellow travelers joining this idiosyncratic project. My gratitude and appreciation go out to all of you.

Eleven New Factors found by Stage 2 of Special Project

Oct 6, 2003: The second stage of the special project has yielded eleven new factors. These factors are listed on the Factors Page with discovery dates from 2003-09-24 through 2003-09-30. The special project uses the Prime95 program to search for factors of all components of M(3326400). The second stage used B1=11K, optimal for 20 digit numbers. Stage 3 is already underway using B1=50K, which is optimal for 25 digit factors.

New ECM Server with ECM5 Thresholds Provided by Japke Rosink aka BotXXX

Oct 2, 2003: Japke Rosink, known as BotXXX on the boards, has updated the ECM Server to match the ECM5 program we are using. When the ECM program changed from version 4 to version 5, there were improvements in the Stage 2 processing. To take full advantage of these improvements, the default value of B2 was increased, especially for larger B1 levels. With these higher B2 values, fewer curves are needed at each level. But the number of curves requested at each level is hard-coded into Tim Charron's ECM Server. Tim provides source code, but I wasn't successful in compiling it. Japke took up the challenge and created a modified version using the Watcom Compiler. For composites under 700 digits, the ElevenSmooth ECM Server is presently using B1=1M. With Japke's changes, the threshold for transition to B1=3M has moved about 750 curves closer. Manually adjusting this many curves to compensate would have been a logistical headache.
THANKS, Japke!

Forty New Factors found by Prime95 Special Project

Sept 23, 2003: The first stage of a special project has yielded forty new factors. These factors are listed on the Factors Page with discovery dates from 2003-09-21 through 2003-09-23. The special project uses the Prime95 program from GIMPS to search for factors of all of M(3326400). As a practical matter, this searches all the Mersenne subfactors with exponents divisible by 25 because the other Mersenne subfactors have already been tested to higher levels through the ecm server. This first stage used B1=2000, optimal for 15 digit numbers. The next stage of this special project will use B1=11000, optimal for 20 digit factors.

Three Factors Plus a Completed Factorization in One Weekend

Sept 16, 2003: "Antiroach" on the boards left his xp2500 overclocked to 3200 running the ecm client program over the weekend and had a lucky streak the found three primes. One of them completed the factorization of M(3520). The new entries for lowM.txt and factoredM.txt are:
M( 4032 )C: 967287298662167339558077202115073
M( 3520 )C: 876842301273103818127810927797272474881
M( 3520 )D
M( 14784 )C: 507649231049494939716780475777

First Factor by external user from ECM Server

Sept 7, 2003:Martin Schroeder, McBryce on the boards, has become the first internet connected person to find a factor through the ECM Servers. Using the alternate server at mandelbrot.dynu.com during a period the main server was down, Martin found the 34 digit factor
M( 9504 )C: 2776202386436268283691901876771457

Will Edgington has been informed and the remain 714 digit composite is now in the ecm servers.

Alternate ECM Server at mandelbrot.dynu.com

Aug 27, 2003: The ECM servers at mandlebrot.dynu.com and wblipp.dynu.com are networked together and can be used as alternates for each other. Both servers are handing out factors of M(3326400) and they keep each other updated using the builtin functions of the ecmserver program. If either server goes down while you are participating, you can edit the ecmclient.cfg file and continue working using the other one - both servers learn about all work reported to either server. Andi314 also has some nice statistics pages. A special thank you to Andreas for his support of the project.