**Moderators:** Jwb52z, CedricVonck, kpearson, Honza, Lupine1647

13 posts
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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.

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.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

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, http://www.loria.fr/~zimmerma/records/ecmnet.html#top10 , so far in 2008.

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, http://www.loria.fr/~zimmerma/records/ecmnet.html#top10 , so far in 2008.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

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

March 8, 2008: Tom Womack, http://tom.womack.net/ , 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, http://www.mersenneforum.org/showthread.php?t=10065 .

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, http://tom.womack.net/ .

Sieving in progressing to finish the C195 from M(2788). You can participate by reserving a range in the thread, http://www.mersenneforum.org/showthread.php?t=10031 .

March 8, 2008: Tom Womack, http://tom.womack.net/ , 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, http://www.mersenneforum.org/showthread.php?t=10065 .

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, http://tom.womack.net/ .

Sieving in progressing to finish the C195 from M(2788). You can participate by reserving a range in the thread, http://www.mersenneforum.org/showthread.php?t=10031 .

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

Womack et al Finishes M(2376)

May 7, 2008: Tom Womack's, http://tom.womack.net/ , 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, http://www.mersenneforum.org/showthread.php?t=10031 .

The factorization announcement, http://www.mersenneforum.org/showthread ... post132964 , 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, http://homes.cerias.purdue.edu/~ssw/cun ... ir60/cun38 .

Thank you to Tom and rest of the team!

May 7, 2008: Tom Womack's, http://tom.womack.net/ , 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, http://www.mersenneforum.org/showthread.php?t=10031 .

The factorization announcement, http://www.mersenneforum.org/showthread ... post132964 , 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, http://homes.cerias.purdue.edu/~ssw/cun ... ir60/cun38 .

Thank you to Tom and rest of the team!

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

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 2^1663200+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 2^3326400-1. 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 factor 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

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 2^1663200+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 2^3326400-1. 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 factor 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

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

BOINC Valentine

Feb 14, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , 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.

Feb 14, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , 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.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

Second yoyo-BOINC factor

Feb 19, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , 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 19, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , 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.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

Third yoyo-BOINC factor

Mar 22, 2009: yoyo@home user [TEMPLAR] Kaar found a P49 from 2^3465-1. 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.

Mar 22, 2009: yoyo@home user [TEMPLAR] Kaar found a P49 from 2^3465-1. 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.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

Largest ECM yet, yoyo's fourth, completes 14th primitive

Mar 27, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , user Aflatoxin found a P51 from 2^3360+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, http://home.earthlink.net/~elevensmooth ... l#complete .

Mar 27, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , user Aflatoxin found a P51 from 2^3360+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, http://home.earthlink.net/~elevensmooth ... l#complete .

Last edited by Jwb52z on Tue Mar 31, 2009 5:53 am, edited 1 time in total.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

Yoyo Completes Another Primitive

Mar 30, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , has completely factored a second primitive in three days. User Marc1 found a P49 from 2^3780+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, http://www.alpertron.com.ar/ECM.HTM . This is the fifteenth primitive for which ElevenSmooth has completed the factorization, http://home.earthlink.net/~elevensmooth ... l#complete .

Mar 30, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , has completely factored a second primitive in three days. User Marc1 found a P49 from 2^3780+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, http://www.alpertron.com.ar/ECM.HTM . This is the fifteenth primitive for which ElevenSmooth has completed the factorization, http://home.earthlink.net/~elevensmooth ... l#complete .

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

One-Two Punch Knocks Out 23080+1 on Easter

Apr 13, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , 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, http://www.alpertron.com.ar/ECM.HTM . This is the sixteenth primitive for which ElevenSmooth has completed the factorization, http://home.earthlink.net/~elevensmooth ... l#complete , and the fourth done by yoyo@home.

Apr 13, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , 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, http://www.alpertron.com.ar/ECM.HTM . This is the sixteenth primitive for which ElevenSmooth has completed the factorization, http://home.earthlink.net/~elevensmooth ... l#complete , and the fourth done by yoyo@home.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

P43 for 26160+1

May 1, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , user [ESL Brigade] NaiV found a P43 that reduced the unfactored primitive of 2^6160+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.

May 1, 2009: yoyo@home, http://www.rechenkraft.net/yoyo/ , user [ESL Brigade] NaiV found a P43 that reduced the unfactored primitive of 2^6160+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.

- Jwb52z
**Posts:**997**Joined:**Tue Aug 30, 2005 10:56 pm

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