Extension to the Base 2 tables from 1300 to 1500, LM to 3000

[Batalov]

Yeah, for this table I did not put "/q" hints (in the last/"comment" column) - because not all of them are.

There are many easy sextics there, but there is no compelling reason to do them right now. (because there will be no credit. All that folks do on xtend tables will go uncredited.)
One should wait for the moment of merge of xtend tables into general tables.

[charybdis]

Does

Originally Posted by Sam Wagstaff

After the numbers in the extension have been factored as thoroughly as the regular Cunningham numbers they will be added to the official tables.

not imply that the extension won't be merged into the main tables until most of the easy sextics are done? Or does that line only apply to ECM efforts?

[Batalov]

The latter. (Usually Sam did that ecm'ming himself; recently he started opening these to the public. You can safely assume that a t55 level is definitely already done on all of these.)

It does also mean a small mix of other methods, especially if/when they are easier than ecm.
E.g. if Sam hits a c200 with a p59, then he runs a small GNFS himself; and so does anyone who previously participated in these pre-extension sprints.
If you ask me, it is a more meaningful weekend hobby job than moving some seven-digit-seed aliquot sequence 2 or 3 steps higher.

[charybdis]

Can confirm that ECM is very much worthwhile:

Input number is 112962684910978005979707883110687425334751394055520879404011959657332843602530827086693504635422750727754158030487431949129607839267073568635226319122113659002180679302496838174314943902966481942043022475798041473053257 (219 digits)
Using B1=400000000, B2=4767896883766, polynomial Dickson(30), sigma=1:950355941
Step 1 took 887735ms
Step 2 took 208937ms
********** Factor found in step 2: 18079030929723990295640293502821337497340759521793530157
Found prime factor of 56 digits: 18079030929723990295640293502821337497340759521793530157
Composite cofactor 6248271013533942187625468605111142926663041596213979398984907236621613347487386335033546137192022175920901985083517768960203749984569259931558968042151449551468301 has 163 digits

[swellman]

Sam now reports running ECM for ~300 curves per number

with B1 ranging from 2e9 for small (~200D) numbers down to 1e9 for large (~400D) numbers.

While I’m still focused on finishing ECM for the remaining 1987 list of base-2 CNs, my plan is to start weaving the new base-2 extensions into the big quilt. I’m thinking of starting with a single pass of 4000 curves @B1=260e6. Then later I can repeat 19000 curves (twice eventually) at the same level. Thoughts?

I was going to queue the new work by increasing number of digits, but willing to take requests. It will take years to get these all up to the just the t60 level. And don’t forget the 1987 list is still in play. This strategy tries to please everyone thus guaranteeing no one will be pleased.

One other observation from Sam

Someone must have tried the 2,n- table, as I found no new factors in it. I found just a few new factors in the 2,n+ tables, but lots of factors in the 2LM table.

Did anyone run some ECM in this patch? Just trying to avoid repeating work.

One last note - I was recently reminded of this page. What’s the protocol here? Best to avoid any numbers on the GIMPS page? Or will any additional “rogue” ECM work be embraced?

[charybdis]

Originally Posted by swellman

Sam now reports running ECM for ~300 curves per number

While I’m still focused on finishing ECM for the remaining 1987 list of base-2 CNs, my plan is to start weaving the new base-2 extensions into the big quilt. I’m thinking of starting with a single pass of 4000 curves @B1=260e6. Then later I can repeat 19000 curves (twice eventually) at the same level. Thoughts?

I was going to queue the new work by increasing number of digits, but willing to take requests. It will take years to get these all up to the just the t60 level. And don’t forget the 1987 list is still in play. This strategy tries to please everyone thus guaranteeing no one will be pleased.

That sounds like a good plan to start out with; in the long term maybe it would be best to move on to 850e6 after the first 19000@260e6, given that Yoyo won't be the only ones running ECM on these numbers.

I've got a few machines running curves on composites below c250, reasoning that if an ECM factor leaves behind a composite cofactor, then it will be within GNFS range - and that's worked out nicely, as you can see above.

One other observation from Sam

Did anyone run some ECM in this patch? Just trying to avoid repeating work.

One last note - I was recently reminded of this page. What’s the protocol here? Best to avoid any numbers on the GIMPS page? Or will any additional “rogue” ECM work be embraced?

The GIMPS work probably explains the lack of factors in the 2- table. Ryan has run a lot of ECM on small Mersennes, but I don't think he's reported all of it to GIMPS, so it would be worth contacting him to get some rough curve counts. I expect the non-Mersenne numbers in the 2- table (those with composite exponents) have not had as much ECM.

[charybdis]

Pleased to see that Sam has credited me with a new record ECM factor

3458  2,2750M c185 33064259907061907187454540598801861343151128939115124241607813225512323356759645078501. p99 Balfour ECM

Edit: fixed now, but it was good while it lasted.