mfaktc: a CUDA program for Mersenne prefactoring

[davieddy]

Originally Posted by TheJudger

What is the expected factor rate once P-1 has been done with reasonable B1/B2 bounds?

Oliver

That question has been excersizing several of us.

In particular, it was decided a few years ago that
it was more efficient to do P-1 before the last worthwhile
bit of TF. I wonder whether the P-1 would then
render the "last bit" not worthwhile.

Of course, you and GPUs have thrown a large spanner in the works

David

[davieddy]

Originally Posted by davieddy

That question has been excersizing several of us.

In particular, it was decided a few years ago that
it was more efficient to do P-1 before the last worthwhile
bit of TF. I wonder whether the P-1 would then
render the "last bit" not worthwhile.

Of course, you and GPUs have thrown a large spanner in the works

David

(Responding to your own post and partially answering the question therein)

There is obviously little to be gained by refining "bit level" for TF
further. (Working near a Max/Min optimum).

But if the "worthwhileness"of the "last bit" was marginal, P-1
would obviously tip it over the edge.

David

[Prime95]

Originally Posted by TheJudger

...checked the exponent status of the first 4 no factor M53.xxx.xxx: all of tham had P-1 done before your TF attempt to 2^70.

What is the expected factor rate once P-1 has been done with reasonable B1/B2 bounds?

Ah, mystery solved! I should have thought of that myself. IIRC, P-1 will find somewhere in the neighborhood of 30-40% of the factors.

[drh]

Originally Posted by Prime95

Ah, mystery solved! I should have thought of that myself. IIRC, P-1 will find somewhere in the neighborhood of 30-40% of the factors.

Out of the hundreds of exponents that I've tested, I only ran a TF on exactly 1 that had a P-1 done on it beforehand, and that only consisted of 2 tests, so I'm not sure this solves the mystery. I'm now at 15 factors on 1495 tests, 1493 before a P-1.

This is all in the 76M range, and there has only been 23 P-1's done in that range, IIRC.

[Prime95]

Originally Posted by drh

I'm now at 15 factors on 1495 tests, 1493 before a P-1.

I think that's unlucky but not suspicious. Xyzzy's was worrisome because it involved 9000 tests.

[drh]

Originally Posted by Prime95

I think that's unlucky but not suspicious. Xyzzy's was worrisome because it involved 9000 tests.

I agree, and just to clarify, a "test" is a single bit level on an exponent, not only counting individual exponents, right? I've got 1495 "tests" on 322 exponents.

[davieddy]

Originally Posted by Prime95

Ah, mystery solved! I should have thought of that myself. IIRC, P-1 will find somewhere in the neighborhood of 30-40% of the factors.

From a "throughput" POV, has TF on GPUs (at least temporarily) made P-1 redundant?

[Prime95]

Originally Posted by davieddy

From a "throughput" POV, has TF on GPUs (at least temporarily) made P-1 redundant?

No. Prime95 will refuse to do P-1 if a number has had so much TF done that P-1 will not be profitable.

I think we'll see a slight reduction in the B1/B2 bounds selected now that more TF is being done.

[davieddy]

Originally Posted by Prime95

No. Prime95 will refuse to do P-1 if a number has had so much TF done that P-1 will not be profitable.

I think we'll see a slight reduction in the B1/B2 bounds selected now that more TF is being done.

Hmm.

1) I think "No" meant "Yes".

2) Without fully understanding P-1, I would have thought
"reduction" meant "increase"!

David

[Christenson]

Originally Posted by Prime95

Ah, mystery solved! I should have thought of that myself. IIRC, P-1 will find somewhere in the neighborhood of 30-40% of the factors.

Or read it here!:
http://mersenneforum.org/showpost.ph...&postcount=971



Sorry I didn't have any numbers....hoping that the extra TF will allow P-1 to look for larger factors...

Anyway, calculation about my narrow view of GIMPS rolled through my head last night...it went like this: Decrease TF cost by factor of ~128, get ~7 extra bit levels....7*~1/70 = 1/10....so 10% more exponents will have factors found, or 10% fewer will need LL and LL-D tests...looks like the big performance increase will need to be in LL, possibly by getting the CPU out of the sieving path for TF and possibly P-1. Got to work on mfaktc this week!

[davieddy]

Originally Posted by Christenson

looks like the big performance increase will need to be in LL

Just look at the "Top Ten" primes

How do you think the top nine were discovered?

David

PS I was wondering for a bit why the latest
discovery was attributed to "G12" when GIMPS has found 13.
I think the explanation is that Cooper and Boone found 2.

Lightning strikes...