July 15, 1998, Nancy (France)
Dear all,
like last month, a short newsletter since I'm (theoretically) on vacation.
Sam Wagstaff reports: from the 19 new factors found in June in the regular
Cunningham tables, 8 were found by ECMNET, and 6 over 7 in extension X7.
Here are the 24 new factors of 30 digits or more found using gmp-ecm that
were reported to me since June 18 (some of them were found before):
152866354235440062064075063357 divides 3*2^244+1 Michael Rödel
152873624211113444108313548197 divides Sm(81) Allan MacLeod
233736323832959557355117667391 divides 3*2^265+1 Michael Rödel
314547891171506427278717744569 divides 10^362+1 Torbjorn Granlund
709534381472277920756448664081 divides 712^60+1 Aiichi Yamasaki
861736561111962549644136452599 divides p101+1 Achim Flammenkamp
3657907521626311613953990373371 divides 871^51+1 Aiichi Yamasaki
4027715748614915368697856477361 divides 833^60+1 Aiichi Yamasaki
5613704088078908539949110911517 divides p143+1 Achim Flammenkamp
5735039483399104015346944564789 divides 177*2^220+1 Michael Rödel
11534030791495532757323558159281 divides 954^60+1 Aiichi Yamasaki
116877740332519011737292886104457 divides 2^1163+1 Bruce Dodson
707285850117624346067550937755073 divides 10^224+1 Torbjorn Granlund
723179476352802400636953428399129 divides 2^1073+1 Bruce Dodson
797198773320048685605704926860121 divides 718^60+1 Aiichi Yamasaki
5342512091349500920639852868215477 divides 10^483+1 Linus Nordberg
7097997192550078754033153026452893 divides p94+1 Achim Flammenkamp
11048413776665718160704624949883741 divides p(19423) Eric Prestemon
2622476816389302805566618482868567341 divides 2^1186+1 Paul Zimmermann
6844495453726387858061775603297883751 divides Sm(113) Allan MacLeod
18223164902649732703974292810329988561 divides p105+1 Achim Flammenkamp
79445908023117847711350146066567930257 divides 2^1031+1 Bruce Dodson
246254302494824359942225692028596828479 divides 10^341-1 Torbjorn Granlund
314293140427626491056008875724151058487007 divides 10^199+1 Torbjorn Granlund
The winner of the month is clearly Torbjorn Granlund, with four large factors
including a new champion of 42 digits (a champion is a factor of 40 digits or
more).
Ecmnet has now some competitors: George Woltman designed a very fast program
for factoring Mersenne numbers. See http://www.mersenne.org/ecm.htm.
This program runs under MSDOS or Linux, and is about 3 times faster than
gmp-ecm! For example, on a PII-300, it needs only about 2 minutes to run
one curve with B1=1000000 on M601. Since end of May, George's program
already found some nice factors, including those of 30 digits or more:
M947 has a factor: 11892980076500863942962129100776937
M1201 has a factor: 2830858618432184648159211485423
M1307 has a factor: 161633497146742177992711798481
M1307 has a factor: 141196558805510033914433414063
M1361 has a factor: 856450061281312036458486309832227737
M1523 has a factor: 182902246957664987166063221498412840793
M1597 has a factor: 46421116904392458242754417331076737
M1741 has a factor: 25269109534063262433544878967583
M1777 has a factor: 113460041673379080737466244127
M2113 has a factor: 101936210855894546221988426464097
M2131 has a factor: 129239458251829470983931962239
M2311 has a factor: 4514379640917651135021865565129
M3461 has a factor: 321172740126659477699594681881
M3469 has a factor: 49099830535845038692501139425951
Finally, some other large factors, including 5 new champions, were found
last month using Peter Montgomery's ecmfft program:
246306661383223563619590775949 divides 2^1774+1 Peter Montgomery
169997665479575625158961736348751 divides p(23087) Bruce Dodson
2743400324920929934072747900058453 divides 2^2014+1 Peter Montgomery
4708253967270778823533486411429633 divides 2^1064+1 Bruce Dodson
22773621472604111191087721187593281 divides 2^1406+1 Peter Montgomery
7201935329692363728844274296784241409 divides 2^1008+1 Bruce Dodson
118310908116219234147550210872300654121 divides 2^1015+1 Bruce Dodson
5340177084869200990999949530063600471907 divides p(25577) Bruce Dodson
4333842025097140661120634098144190031735501 divides 2^1186+1 Peter Montgomery
81395755904416856900065674738927988961556601 divides p(25541) Bruce Dodson
93307098374124113202539861425790061962795219659 divides p(15461) Bruce Dodson
1078825191548640568143407841173742460493739682993 divides 2^1071+1 Paul Z.
The above 49-digit prime is the largest factor found by ecm so far, and the
47-digit factor of p(15461) from Bruce Dodson is the 3rd largest one.
Therefore, it seems to me that the original goal of the ecmnet project,
i.e. find the first factor of 50 digits or more by ecm, is now very close.
Perhaps this huge factor won't be found by gmp-ecm, but with all excellent
programs that are available today, I bet it will be found in 1998!
Once again, many thanks to all of you who participate to ecmnet, and
please send me new factors for the top-100 (now only 29 digits or more).
Paul Zimmermann