Index 1 Sequence Work for the "n^i" Aliquot Project

[gd_barnes]

In this thread, when I say something is fully ECM'd, it means I've done it to 31% of factor size. That's generally been my standard for anything <= 145 digits. I've only fully ECM'd C<=135 with the index 1 effort plus there are some that I had fully ECM'd prior to this effort that are in the low 140s that happened to show up here.

All that said, the above is likely too much for > ~145 digits from what I've read.

Consideration: ECM using the default in the the aliqueit.ini file: factor size * .235 + 9.4.

We definitely need to run a lot of these to t45. Based on the aliqueit.ini formula above, anything C>150 would need almost that full amount or more. C144-150...somewhere between t40 and t45.

In the long run, based on all past postings I've seen, you should get slightly more splits per hour or per day by running ECM to the optimal depth, whatever that depth happens to be. Of course in the short run you might have very good or bad luck.

Even at only 12-15% splits when running from t35 to t40, I was clearly getting more splits per day than had I tried to run NFS on some of those. Of course it will be more challenging for t40 to t45, time-wise.

[gd_barnes]

Ed, how about I finish up the ECM from t35 to t40 for the 90s? I'm averaging about 4 of these per hour on the Ryzen. I see that there are ~30 sequences remaining for bases 94 to 99. I could knock those out in 7-8 hours and we would be done with ECM to t40 on everything.

[gd_barnes]

Originally Posted by EdH

Hmm, 105^93 gave up a 40 digit factor under t45 ECM in about 2 hours. NFS would have taken about 3 hours. But, the ECM work took some of the clients away from the NFS work, so I'd need to study these times more to see if t45 is worth it at this level. Obviously, it saves time if successful, but . . .

That's slightly bad luck on my part that I didn't catch that one on my t40 effort. If it had caught it, it would have only taken ~15 mins. :-)

[EdH]

Originally Posted by gd_barnes

Ed, how about I finish up the ECM from t35 to t40 for the 90s? I'm averaging about 4 of these per hour on the Ryzen. I see that there are ~30 sequences remaining for bases 94 to 99. I could knock those out in 7-8 hours and we would be done with ECM to t40 on everything.

I completed my run through 99^99 at t40, so we should be all done. I see I only mentioned queing it up, but not completing it.

[gd_barnes]

Originally Posted by EdH

I completed my run through 99^99 at t40, so we should be all done. I see I only mentioned queing it up, but not completing it.

Great! Good to know we have that phase done.

[gd_barnes]

Taking all of the C134s. Time to be done with this phase of index 1.

[EdH]

Originally Posted by gd_barnes

Taking all of the C134s. Time to be done with this phase of index 1.

[VBCurtis]

Originally Posted by EdH

The GPU has 896 cores (at least that's what GMP-ECM says). I built all my efforts around that number of curves. These are my B1 values for t-levels:

t18 - 1e3
t25 - 15e3
t30 - 12e4
t35 - 1e6
t40 - 6e6
t45 - 5e7
t50 - 4e8
t55 - 2e9
t60 - 2e10

This gives me one GPU pass for each level and the residues are handled by a different machine with lots more threads.

If I were working around a GPU as you are, I'd do up to T30 on CPU before getting a GPU involved at all.
1e6 for T35 is good.
I'd use 8e6 for T40, or I'd stick with 6e6 but send "-k 2" to GMP-ECM for stage 2 to run bigger and faster than it does with 6e6. k=6 on a smaller B2-chunk (default) is slower than k=2 on a bigger B2-chunk, even though the latter is 30% bigger B2. Alternately, you could manually set the larger B2 for your stage 2, and GMP-ECM will select k=2.

For T45, I'd do 2 runs of B1=2e7. 34e6 is also pretty fast (in terms of expected time to find a 45-digit factor in stage 2), if you prefer having different B1's for each step you could use 2e7 and 34e6. I think I like this better than two 2e7 runs, actually.

T50 is fastest at 6e7, with 8e7 close to same speed. Since many composites are a size where you'd want a portion of a T50 anyway, I think I'd do a run at 6e7, one at 8e7, then one at 15e7. The 15e7 is the right size for T55, too....
If I want more of a T55, I'd do a second or even a third run at 15e7 before going bigger, and bigger would be 3e8 or 42e7 or 65e7, but those are sizes fast for finding a 60 digit factor rather than 55 digit.

Advantage: Shorter GPU runs that have strong chances to find a factor, so less wasted GPU effort on stage1's that you never use stage2 on. Also, easier to have steps that are portions of a T45 or T50.

Raising B1 too quickly leaves you doing curves rather inefficient for the T-level you're targeting; but if you're going to do a T60 or T65 anyway there's merit in skipping from e.g. T40 to T50 to T60 directly, or only doing enough curves for 25-35% of a T-level before going up. So, if you wanted a T50, you might do a GPU run at 1e6, then 8e6, then 2e7, then 6e7 and 8e7, ending with 15e7. If you want less than a T50 you might omit 15e7 and end up with something like T48 = half a T50.
Note that 6e7 + 8e7 + 15e7 will finish all 3 runs before the 4e8 finishes to get to T50.

[EdH]

Wow! Excellent! I'll work on my scripts today. And, last night I successfully got my larger GPU running GMP-ECM. I'll work with these values when I set it up with its scripts. Thank You for all that work figuring out the best use numbers.

[gd_barnes]

All of the C134s are done.

All sequences with cofactor C<145 digits have been cleared.

[EdH]

Excellent! I'll try to update post #1 tonight. My c145 work will take slightly longer. . .