[QUOTE=Andi47;100042]A pp51 with B1 = 3M - WOW![/QUOTE]That was my reaction.


Paul

The lucky group order is
2^2 3^2 5 11 19 41 47 139 149 6301 25643 41969 226103 336403 2890301 191914903

Congrats!

Alex

[QUOTE=Andi47;100042]A pp51 with B1 = 3M - WOW![/QUOTE]

Agreed! Perhaps it's worth keeping track of large ecm factors
found with small limits. For B1 = 11M, we have the first ecm
prime factor of 50-or-more, Curry's p53
([url]http://www.loria.fr/%7Ezimmerma/records/p53)[/url]. The record that
replaced that was a p54 found in step 1(!!), with largest group order
factor of 13323719, and the B1 used was 15M --- the second largest
was 9.839M, so B1 = 11M would also have worked (easily).
(cf. [url]http://www.loria.fr/%7Ezimmerma/records/p54[/url])
For B1 = 43M, there's my p61 factor last year. These seem to be
reasons to believe that neither B1 = 110M nor (much less!) B1 = 260M
have reached their potential yet. On to 256-bit prime ecm factors!
-Bruce (congratulations to Greg, and seems like Paul/xilman deserves
a shout-out as well.)

Three More results
 

[QUOTE=R.D. Silverman;99668]5,3,244+ C142 = p41.p101

94444153383610016065099207989656900925193

11864397782556880111954414898119162292473191509774866434362653622235777715298268261429439840494178801

I will start filtering 5,4,239- tonight. 5,3,241- is in progress. 5,3,247+
will be next.[/QUOTE]

5,4,239- C121 = p54.p68

363091231282992237448699612976873074506541781174196371
21443810114945014745895620833365926511397690249830327067406633026261

5,4,241- C147 = p62.p86

10839545721050256188023120358496772228646805057493978753258211
61736620090419915579750883186619836392112347509559127811991409483784723896192931666129


5,3,247+ C129 = p51.p79

573851211397285658797030790222222715995211352275617
1445142488345321960188821200847028094105337880278976387225345768594277535856501


5,4,247- is in progress. 5,3,248+ and 5,4,248+ will be next

Found this with GMP-ECM:

5,3,287+ has a factor:

Run 331 out of 500:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=169662704
Step 1 took 109516ms
Step 2 took 56141ms
********** Factor found in step 2: 131259030985897438370460031873601381589745219
Found probable prime factor of 45 digits: 131259030985897438370460031873601381589745219
Probable prime cofactor ((5^287+3^287)/2297/4156909/906934351/2627365505987918123/1408933212044372800728976013/80312/83/68486046875179831736329427)/131259030985897438370460031873601381589745219 has 60 digits

3^491 - 2^491 has a pp43 factor 3024433728225651855753472770183675882153097 and the remaining cofactor is prime.

So 3^491 - 2^491 =

983 *
14731 *
8652403 *
80114126693081639 *
391170997726902204479 *
1580657495893687538646673 *
810715655322221294808618280382927 *
3024433728225651855753472770183675882153097 *
121391260968618904993875833244588614076710032779705104154197074140717594929579538643

[annoyingly, I did this in two weeks with gnfs rather than with ecm]

Has anyone got a better def-par.txt for ggnfs for the 120-135-digit range? I suspect the factor base used in this case (primes less than 5400000) was significantly smaller than optimal.

Updates
 

The web pages and ECMNET server have just been updated. There are 16 new factorizations, all but one complete, and only 128 composites left in the tables now. When that figure has fallen to 30 or so, I'll add some more extensions to the tables.

Tom is now getting email direct from the ECMNET server when it is told of a factor, so he should find it a little easier to keep his reservation system current.

Paul

5,4,247-
 

[QUOTE=R.D. Silverman;100148]5,4,239- C121 = p54.p68

363091231282992237448699612976873074506541781174196371
21443810114945014745895620833365926511397690249830327067406633026261

5,4,241- C147 = p62.p86

10839545721050256188023120358496772228646805057493978753258211
61736620090419915579750883186619836392112347509559127811991409483784723896192931666129


5,3,247+ C129 = p51.p79

573851211397285658797030790222222715995211352275617
1445142488345321960188821200847028094105337880278976387225345768594277535856501


5,4,247- is in progress. 5,3,248+ and 5,4,248+ will be next[/QUOTE]



Here is 5,4,247- c134 = p50.p84

35139782877004826556372791701231871826433859646041
596213121442577638550251041508094962483211387452984951895137923379487001810837156889

I have started the filtering for 5,4,248+ and 5,3,248+ is sieving.

6,5,229+ and 3,2,403- will be next.

Bob

5,4,248+
 

[QUOTE=R.D. Silverman;100907]Here is 5,4,247- c134 = p50.p84

35139782877004826556372791701231871826433859646041
596213121442577638550251041508094962483211387452984951895137923379487001810837156889

I have started the filtering for 5,4,248+ and 5,3,248+ is sieving.

6,5,229+ and 3,2,403- will be next.

Bob[/QUOTE]


Here is 5,4,248+ C139

42302337811455239515394219882503802224832902741397248444769
175762777795522593044586112173402479692327549043858538141720372500653810135344929

5,3,248+ will finish sieving this weekend, which will finish 5,2, 5,3, and 5,4
to exponent 250.

6,5,229+ is in progress.

[QUOTE=R.D. Silverman;101073]Here is 5,4,248+ C139

42302337811455239515394219882503802224832902741397248444769
175762777795522593044586112173402479692327549043858538141720372500653810135344929

5,3,248+ will finish sieving this weekend, which will finish 5,2, 5,3, and 5,4
to exponent 250.

6,5,229+ is in progress.[/QUOTE]

I finished this last week but forgot to post it.

5,3,248+ c115 = p56.p59

36889369180578447344872196777911563959867609127551227457
48366998473997438055356143046418022191556063405630503252001


3,2,403- is about 90% sieved. 6,5,229+ is about 75% done.
6,5,232+ will be next.

[QUOTE=R.D. Silverman;102127]I finished this last week but forgot to post it.

5,3,248+ c115 = p56.p59

36889369180578447344872196777911563959867609127551227457
48366998473997438055356143046418022191556063405630503252001


3,2,403- is about 90% sieved. 6,5,229+ is about 75% done.
6,5,232+ will be next.[/QUOTE]

Here is 3,2,403- C151 = p45.p106

987181561950506928972744054925015604731086073

1347554579979565353610087203935075781206952880101757908044334156103650470019517487990193757517800438110043


I am running the linear algebra for 6,5,229+ now.

I have acquired access to a small number of machines. It's not much
(about 6) but it should be enough to let me work on the smaller
Cunningham composites. I am therefore stopping work on these numbers
for the time being. I will next do 5,423+.