mersenneforum.org - Factoring humongous Cunningham numbers

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[QUOTE=Andi47;109349]The webpages seem to have just crashed. (I was able to enter the main page, but when clicking to e.g. the 7 tables or retrying the main page, I get errors - server not found.)[/QUOTE]This particular one was caused by my ISP having a DNSoutage. Screwed me over in many ways. Appears to be fixed again.

The ECMNET server also hanged. That, I believe, came about because it was flooded with incoming connections, many of them with reports of new factors. Well over a hundred factors are known already. Two more arrived while typing this posting!

Paul

7,2,186+ has a factor:

Run 103 out of 401:
Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=3342042654
Step 1 took 3219ms
Step 2 took 2891ms
********** Factor found in step 2: 4333779592263461844552282361
Found probable prime factor of 28 digits: 4333779592263461844552282361
Probable prime cofactor 154518177862382477460267701143273362562240688470079917616332528550701 has 69 digits

another one:

7,2,207+ has a factor:
Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=1899581393
Step 1 took 3719ms
Step 2 took 2953ms
********** Factor found in step 2: 15386143618036330577407
Found probable prime factor of 23 digits: 15386143618036330577407
Composite cofactor 1354624657319816644670256226569853300580715591770956739023344948710015459497 has 76 digits

edit2: mpqs on the c76 results:

Sat Jun 30 17:52:02 2007 prp34 factor: 1095237139523685720921757438098391
Sat Jun 30 17:52:02 2007 prp43 factor: 1236832288127973385134314433591117311850367
Sat Jun 30 17:52:02 2007 elapsed time 00:08:00

7,2,201+ c103: done 77 ecm curves with B1 = 11k and 401 curves with B1 = 250k, no factor found. Reserving this number for QS.

[QUOTE=Andi47;109360]7,2,201+ c103: done 77 ecm curves with B1 = 11k and 401 curves with B1 = 250k, no factor found. Reserving this number for QS.[/QUOTE]Fair enough, but I repeat my general warning: ECM is finding factors at a very fast rate and I'd advise the users of MPQS and NFS to hold off for a few days.

Anyone who would like advice and/or assistance on setting up an ECMNET client please email me (paul@leyland.vispa.com) or PM me and I'll do my best to help.

Paul

From ECMNET client:

[code][2007-06-30 21:40:08 GMT] a: Factor found! 9+2_182 / (probable) 127484896987684923820627680733 B1: 250000 sigma: 3906246785 (found in step 2)
[2007-06-30 21:40:08 GMT] a: Co-factor: 9+2_182 / (Probable) 870772178905721496010111027422865963388438033754893161911747548677
[2007-07-01 00:00:20 GMT] a: Factor found! 7+6_190 / (probable) 3906057478414457365973294504474701 B1: 250000 sigma: 918770265 (found in step 2)
[2007-07-01 00:00:20 GMT] a: Co-factor: 7+6_190 / (Probable) 18468600199638006207363974065525137340175754703377636513301
[2007-07-01 00:39:28 GMT] a: Factor found! 9+2_155 / (probable) 7649944403228258099523078276703001 B1: 250000 sigma: 928732308 (found in step 2)
[2007-07-01 00:39:28 GMT] a: Co-factor: 9+2_155 / (Probable) 2110280919201999167887108204393525657226162812544971791877561
[2007-07-01 00:42:31 GMT] a: Factor found! 9-5_183 / (probable) 20389942070101269457699 B1: 250000 sigma: 1208361272 (found in step 1)
[2007-07-01 00:42:31 GMT] a: Co-factor: 9-5_183 / (Probable) 4294057726542287162318818112614473469306123897370040281593787199432836599
[2007-07-01 00:57:18 GMT] a: Factor found! 7+5_203 / (probable) 124487521012353038457543221 B1: 250000 sigma: 188963133 (found in step 2)
[2007-07-01 00:57:18 GMT] a: Co-factor: 7+5_203 / (Probable) 977625689185439546735861795187544016511498089146009170536956368357739
[2007-07-01 01:25:00 GMT] a: Factor found! 9+5_167 / (probable) 6480509760614271291274461635458747 B1: 250000 sigma: 1918576869 (found in step 2)
[2007-07-01 01:25:00 GMT] a: Co-factor: 9+5_167 / (Probable) 694736030914113780899054437371645577202986817182692493904748167
[2007-07-01 10:16:45 GMT] a: Factor found! 7+6_222 / (probable) 154410327194043524318046248401 B1: 250000 sigma: 3729491635 (found in step 2)
[2007-07-01 10:16:45 GMT] a: Co-factor: 7+6_222 / (Composite) 7836636343659899205474330532604938499633801374157438136575474108262161326947466502221
[2007-07-01 10:26:31 GMT] a: Factor found! 8+5_161 / (probable) 332872282759741563284764459 B1: 3000000 sigma: 0 (found in step 2)
[2007-07-01 10:26:31 GMT] a: Co-factor: 8+5_161 / (Probable) 759557374351167046543983103851911419078456203261569772293905288402783126846584323228880199819

[/code]Paul,

I found 8 of them and 6 were double checks!!! That's really a waste of time. The server should purge the results. Can you please check what's going on?

Regards,

Carlos

[QUOTE=em99010pepe;109382]
I found 8 of them and 6 were double checks!!! That's really a waste of time. The server should purge the results. Can you please check what's going on?

Regards,

Carlos[/QUOTE]I know exactly what's going on and the server does purge the results.

However, when there are lots of clients connecting to a server, the server can hand out the same uunfactored number to several clients. As soon as the factor comes back, the composite is not handed out again, though if the cofactor is composite that number is itself added to the server.

Under normal circumstances this behaviour is justified --- almost all the time a client does not find a factor. Occasionally two clients will find [i]different[/i] factors of the same number. This has happened several times in the last 24 hours.

These are not normal circumstances. I processed about 240 emails last night and another 255 are waiting in my inbox to be processed this morning. Tom Womack, who also gets a copy of the ECMNET mail so he can maintain his reservation system, is similarly flooded.

All will settle down in a day or two.

Paul

[QUOTE=xilman;109384]Under normal circumstances this behaviour is justified --- almost all the time a client does not find a factor. Occasionally two clients will find [i]different[/i] factors of the same number. This has happened several times in the last 24 hours.[/QUOTE]

Is the strategy configured to reduce the likelihood of a number being sent out multiple times? Or are there too many ECMNet users that strategy isn't helpful?

Did you have an ECMNet server for Cullens and Woodalls (or the Generalized form of said numbers)? I ask because if you have too many clients for this project, maybe some of the users would be interested in helping on those projects.

[QUOTE=rogue;109389]Is the strategy configured to reduce the likelihood of a number being sent out multiple times? Or are there too many ECMNet users that strategy isn't helpful?

Did you have an ECMNet server for Cullens and Woodalls (or the Generalized form of said numbers)? I ask because if you have too many clients for this project, maybe some of the users would be interested in helping on those projects.[/QUOTE]The configuration is primarily to send out the number with the smallest number of completed curves at the B1 level currently the smallest to be used. There's a random element superimposed on this behaviour too.

Almost all the time that strategy works well. Only when large quantities with very small factors and very small B1 (so each curve doesn't take long compared with the client's time between server contacts) and when there are a fair number of clients does this generate duplicate factors. As I said, these are not normal circumstance. I doubt whether we'll see many duplicate factors from now on, except from runts that have been finished with MPQS or NFS and I've not had chance to disable them on the server. There are a dozen or so in that category right now. Another reason why I suggest the MPQS/NFS people hang off for a few days.

Paul

[QUOTE=xilman;109390]The configuration is primarily to send out the number with the smallest number of completed curves at the B1 level currently the smallest to be used. There's a random element superimposed on this behaviour too.

Almost all the time that strategy works well. Only when large quantities with very small factors and very small B1 (so each curve doesn't take long compared with the client's time between server contacts) and when there are a fair number of clients does this generate duplicate factors. As I said, these are not normal circumstance. I doubt whether we'll see many duplicate factors from now on, except from runts that have been finished with MPQS or NFS and I've not had chance to disable them on the server. There are a dozen or so in that category right now. Another reason why I suggest the MPQS/NFS people hang off for a few days.

Paul[/QUOTE]

I accidently missed sending Paul some of my results. I have done
quite a few of 8,3, 8,5, and 8,7 for exponent < 175 that are currently
listed as composite. I have some 9,k results for exponent < 175 as well.

However, I am on vacation and the results are back in my office.

Here is one result, however:

8,3,173+

173 (1) 347.18347570944674607.63005602635612683515953209759008058770361148593243.388944687670146443606795829904094087414369697136047603232243192477024865140108477192783

I have done all of 8,3+ for exponent < 175 except for 172.
It is an easy C95 and I will leave it for someone else.

@Paul:

A small bug (or two) crept into the update file:

I found the factors of 7,2,286+ c96 and 7,2,207+ c98 with ECM, not MPQS, the only factor which I found with QS yesterday was the factor of the remaining 7,2,207+ c76.

P.S.: What does the statement in this line (bold font) in the update file mean?

[code]7+2 207 C76 [b]10952371395236857209217+2 7438098391.[/b] P43 A Schindel MPQS 2007-06-30[/code]

I guess, this line is intended to say "1095237139523685720921757438098391*p43"?