I have found this factor of 3,2,419- by ecm:

Run 122 out of 200:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=630751143
Step 1 took 299141ms
Step 2 took 144078ms
********** Factor found in step 2: 14609468045540856783864234788403551523670223
Found probable prime factor of 44 digits: 14609468045540856783864234788403551523670223
Probable prime cofactor ((3^419-2^419)/839/38431800507311019576311/133815968776860349833596336711347)/14609468045540856783864234788403551523670223 has 100 digits

I have also emailed this factor to Paul.

[QUOTE=bdodson;108872]
On the substance, I'm not sure that we ought to be surprized that
leading edge computations are no longer leading edge 8 years later!
Today we ought to be thinking about getting access and then routine
access to lots of processors with 4Gb, not 2Gb. Cf 77-digit prime
(256-bit) ecm factors and factor bases for 768-bit gnfs. -bd
[/QUOTE]

Eight years from needing a $10M Cray to needing a $400 desktop is an awful lot faster than Moore's Law would suggest, though I suppose the right deduction from that is that you didn't need something as big as the Cray ... indeed, after a bit of digging I find that something like an AlphaServer DS20 was available at the time and could hold even 4GB of RAM. But nine days on one CPU of what I think was then a fairly elderly Cray was probably easier to come by than a month on the whole of what was then a new high-end server.

[QUOTE=Andi47;109067]I have found this factor of 3,2,419- by ecm:

Run 122 out of 200:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=630751143
Step 1 took 299141ms
Step 2 took 144078ms
********** Factor found in step 2: 14609468045540856783864234788403551523670223
Found probable prime factor of 44 digits: 14609468045540856783864234788403551523670223
Probable prime cofactor ((3^419-2^419)/839/38431800507311019576311/133815968776860349833596336711347)/14609468045540856783864234788403551523670223 has 100 digits

I have also emailed this factor to Paul.[/QUOTE]

Very timely! That was going to be my next reservation. :smile:

[QUOTE=xilman;107179]Another update just posted, this with 9 more completed factorizations. There are only 14 more to go before I add some extension tables.
[/QUOTE]

If I counted correctly, the count of unfactored numbers in the table has dropped to 47.

[QUOTE=Andi47;109239]If I counted correctly, the count of unfactored numbers in the table has dropped to 47.[/QUOTE]Ok, I can take a hint.

I'll post an update this weekend if I get the chance and if the above estimate is correct, add some extensions.

Paul

[QUOTE=xilman;109260]if the above estimate is correct, add some extensions.
[/QUOTE]

According to Tom's table, it is. I submitted one earlier today, and a quick paste into Excel reveals 46 left. And an extension is timely, too. As it stands now, the easiest available GNFS is a C144, and the easiest available SNFS has a difficulty of C201.

Greg

[QUOTE=xilman;109260]Ok, I can take a hint.

I'll post an update this weekend if I get the chance and if the above estimate is correct, add some extensions.

Paul[/QUOTE]

I have some results from 7,k +/-, 8,k +/- and 9,k +/- that you probably
are missing. I will send them after you post.

Base 7,8 and 9 tables extended
 

[QUOTE=R.D. Silverman;109295]I have some results from 7,k +/-, 8,k +/- and 9,k +/- that you probably
are missing. I will send them after you post.[/QUOTE]
I have added extensions for the base 7, 8 and 9 tables. The web page and the ECMNET server have both been updated and I've mailed Tom so he can decide how best to update his reservation page.

Bob's results yielded 67 factors unknown to me and, at the time of writing, the ECMNET clients have already found three more. Accordingly, I suggest that the NFS and MPQS people hold off for a few days while the very small factors are cleared out.


Paul

[QUOTE=xilman;109348]I have added extensions for the base 7, 8 and 9 tables. The web page and the ECMNET server have both been updated and I've mailed Tom so he can decide how best to update his reservation page.

Bob's results yielded 67 factors unknown to me and, at the time of writing, the ECMNET clients have already found three more. Accordingly, I suggest that the NFS and MPQS people hold off for a few days while the very small factors are cleared out.


Paul[/QUOTE]

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=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]

The Webpage is working properly again.

found something....

7,2,219- has a factor:

********** Factor found in step 2: 478974304065388307181253
Found probable prime factor of 24 digits: 478974304065388307181253
Probable prime cofactor 21788637490302096164391386325889703188153938209989240107874517632903640424360566106811 has 86 digits