Factoring humongous Cunningham numbers

[unconnected]

4^478+3^478

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1076126931
Step 1 took 76586ms
Step 2 took 25858ms
********** Factor found in step 2: 25478713955081128075129425301072558393
Found probable prime factor of 38 digits: 25478713955081128075129425301072558393
Probable  prime cofactor <...>  has 134 digits

[unconnected]

4^497+3^497

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2613403821
Step 1 took 116611ms
Step 2 took 34616ms
********** Factor found in step 2: 1472732572014557559668655009592772550262357
Found probable prime factor of 43 digits: 1472732572014557559668655009592772550262357
Probable prime cofactor <...> has 204 digits

4^479+3^479

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3683398723
Step 1 took 84480ms
Step 2 took 26600ms
********** Factor found in step 2: 552552760278600787882923184954703979019
Found probable prime factor of 39 digits: 552552760278600787882923184954703979019
Probable prime cofactor <...> has 182 digits

4^509+3^509

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1735923627
Step 1 took 86071ms
Step 2 took 26817ms
********** Factor found in step 2: 7483717205554360329506414542524255715975177
Found probable prime factor of 43 digits: 7483717205554360329506414542524255715975177
Probable prime cofactor <...> has 178 digits

[unconnected]

6^367+5^367

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=878250290
Step 1 took 236329ms
Step 2 took 62723ms
********** Factor found in step 2: 2007988935432053267351508764511040826381
Found probable prime factor of 40 digits: 2007988935432053267351508764511040826381
Composite cofactor <...> has 226 digits

6^332+5^332

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2443917878
Step 1 took 190655ms
Step 2 took 53879ms
********** Factor found in step 2: 51066218394703665002106753433506525877171697
Found probable prime factor of 44 digits: 51066218394703665002106753433506525877171697
Composite cofactor <...> has 189 digits

4^444+3^444 by SNFS

prp101 = 5725473518918668464331261289814618230078456868486404263163475995917497285235083259471991173547493331
3
prp70 = 3101880939017758685252456874160396714383240864650180767529644644647761

[jyb]

As part of preparing an ECMnet server to coordinate work on these numbers, I'm trying to gather information on ECM work done up to now. Can anybody who has done any non-trivial work since Paul posted the extensions on April 1 please let me know, either here or by PM?

I'm looking for which composites you attacked, the B1 value, and a rough number of curves. Any work done on numbers which are now fully factored need not be included.

I'm particularly interested in hearing from the following people, since you'll all done enough work to actually find factors via ECM:

C Pinho
L Morelli
S Batalov
G Childers
D Domanov

Thanks!

[pinhodecarlos]

Jon,

I didn't track down the night test work I've done when I fired 4 cores to ecm the first release of the comps file April 1 at B1=43000000.

Sorry for any inconvenience. I would be glad to help if an ecmserver could be setup.


Carlos

[Batalov]

I haven't run any heavy ECM to be accounted for.
Just a few dozen 11e6 (and on some runs 22e6) curves on the largest 50; then on another day, the next to last batch of 50; and then on the third to last batch of 50. Nothing heavy.

[frmky]

I've run 832 param=3 curves at B1=11e6 and default B2 on all composites < 2^506 and the 200 largest composites.

[debrouxl]

Like Carlos, I'd lend a hand if there were an ECMNet server, though I can only contribute using modest resources now.

[unconnected]

6^379-5^379

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1943283406
Step 1 took 64278ms
Step 2 took 19786ms
********** Factor found in step 2: 24535180973312724275378619370020426582621927499
Found probable prime factor of 47 digits: 24535180973312724275378619370020426582621927499
Composite cofactor <...> has 153 digits

6^365-5^365

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=844019092
Step 1 took 57979ms
Step 2 took 18146ms
********** Factor found in step 2: 1119658295217018414322203070131526689516941501
Found probable prime factor of 46 digits: 1119658295217018414322203070131526689516941501
Probable prime cofactor <...> has 116 digits

6^347-5^347

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3481389928
Step 1 took 107720ms
Step 2 took 37312ms
********** Factor found in step 2: 8499944091018704815216784808107297307640183
Found probable prime factor of 43 digits: 8499944091018704815216784808107297307640183
Probable prime cofactor <...> has 198 digits

[unconnected]

Originally Posted by jyb

As part of preparing an ECMnet server to coordinate work on these numbers, I'm trying to gather information on ECM work done up to now. Can anybody who has done any non-trivial work since Paul posted the extensions on April 1 please let me know, either here or by PM?

I'm looking for which composites you attacked, the B1 value, and a rough number of curves. Any work done on numbers which are now fully factored need not be included.

I'm particularly interested in hearing from the following people, since you'll all done enough work to actually find factors via ECM:

C Pinho
L Morelli
S Batalov
G Childers
D Domanov

Thanks!

I've run 2000@11e6 on all 4-3, 4+3, 6+5, 6-5 numbers.

[unconnected]

6^341-5^341

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=11379166
Step 1 took 50225ms
Step 2 took 17089ms
********** Factor found in step 2: 2494819749577470254678307040316031692655701
Found probable prime factor of 43 digits: 2494819749577470254678307040316031692655701
Probable prime cofactor <...> has 120 digits