P-1 factoring anyone?

[Prime95]

Originally Posted by ckdo

in my tests P-1 took about 5 times as long as the last 2 bits of TF with a chance of finding a factor less than 3 times as high...

I'll have to look at this more closely. Perhaps, it would be better to delay only the last bit level of TF.

My other idea is to assign randomly assign either P-1 or LL to "makes most sense" computers that will let prime95 use more than the minimum amount of memory.

[Mr. P-1]

Originally Posted by ckdo

BTW in my tests P-1 took about 5 times as long as the last 2 bits of TF with a chance of finding a factor less than 3 times as high...

Originally Posted by Prime95

I'll have to look at this more closely. Perhaps, it would be better to delay only the last bit level of TF.

This is extremely hard to optimise, given the differing performances for the two types of work between differing processors, and between different amounts of memory available to the same processor.

If the TF effort is being held back by P-1, then it might make sense not to do this optimisation at all

My other idea is to assign randomly assign either P-1 or LL to "makes most sense" computers that will let prime95 use more than the minimum amount of memory.

That's very logical. I would prepare to receive complaints though.

[henryzz]

Surely "makes most sense" should give out what makes most sense to computers with lots of memory assigned not just ll tests. It's somewhat in the name of the worktype.

[James Heinrich]

If you want to encourage more people to sign up for P-1, and especially in a useful way, I propose that changing the credit for finding a P-1 factor could help. My proposal is that P-1_nofactor gets credit exactly as it does now, but P-1_factor would get the current credit plus the credit of (one) LL test that now doesn't need to be done. This would mean that you have a (roughly) 1:20 chance of getting 20:1 credit for the work you do. Or looked at another way, a 1:20 chance of getting a 100GHz-days "bonus" for each P-1 assignment completed (based on current exponents (50M = ~5GHz-days for P-1; ~107GHz-days for LL)). This would certainly appeal to the just-in-it-for-the-credits crowd. It would encourage people not only to do P-1, but to do it in a way that increases their chances of finding factors (e.g. assigning more memory).

Assigning P-1 to "whatever-makes-sense" clients is perfectly valid (if they have generous memory allocted), but may catch some users off-guard when Prime95 suddenly starts using lots of memory when it didn't before. I suggest that is something that may need to be done as a last resort, but encouraging (perhaps even bribing, as per my suggestion above) users to volunteer for P-1 is preferred.

[petrw1]

Originally Posted by James Heinrich

My proposal is that ... P-1_factor would get the current credit plus the credit of (one) LL test that now doesn't need to be done.

This concerns me somewhat. It's not a big leap for someone to suggest that anyone who finds a TF Factor is also saving LL tests; and should get the LL credit. And considering LMH is in the 360M range we are WAY over 100 credits.

Assigning P-1 to "whatever-makes-sense" clients is perfectly valid (if they have generous memory allocted), but may catch some users off-guard when Prime95 suddenly starts using lots of memory when it didn't before.

Was this an issue under v4 where by the luck of the draw one could end up doing a P-1 before a LL? It happened to me several times and I just accepted it as part of the "deal".

I guess I am saying my vote is:
1. Ask nicely for more people to voluntarily do P-1
2. Make it part of "do whatever makes sense" for machines with adequate memory allocated. I mean, if I purposely allocate 400Mb to Prime95 I should be prepared to allow Prime95 to use it when necessary.

[davieddy]

Originally Posted by ckdo

BTW in my tests P-1 took about 5 times as long as the last 2 bits of TF with a chance of finding a factor less than 3 times as high...

Is it not something of a remarkable coincidence that P-1 is so
near the borderline of what is worthwhile before LL testing?

The main incentive must be that finding a factor is more satisfying
than merely proving composite.

But "bottleneck"? GIMPS progress would hardly be dented if P-1 had
never been invented.

David

[Prime95]

Originally Posted by davieddy

But "bottleneck"? GIMPS progress ...

An interesting take.

P-1 is (or will be) a bottleneck to GIMPS' orderly workflow. Those signing up for LL tests only will be given exponents that need P-1 and 2 bits of TF as well as an LL test.

The bottleneck to GIMPS' overall progress has been and always will be LL testing (both first time and double-checking).

[ET_]

With a quad core (or my previous 4 PCs) I usually took one LL/DC, one TF (low memory requirements), one P-1 and one ECM/ECM-F (high memory requirements).

If a quad-core requests what makes most sense, there could be a policy for such assignment. Or next client may check for the total available amount of physical memory and consequently behave...

Luigi

[cheesehead]

Originally Posted by Prime95

P-1 is (or will be) a bottleneck to GIMPS' orderly workflow.

... for certain definitions of "orderly", that is ...

Those signing up for LL tests only will be given exponents that need P-1 and 2 bits of TF as well as an LL test.

... which differs qualitatively from what they might well have experienced with the v4 server, how?

It's only the more particular set of choices available from the v5 server that has changed, really. Was there any general opinion that P-1 was a "bottleneck" a year ago when it was usually performed as a default step just prior to LL on the exponent one had been assigned?

The bottleneck to GIMPS' overall progress has been and always will be LL testing (both first time and double-checking).

Yes, we need to find a way to eliminate or at least streamline that lengthy LL testing!

(Personally, I think the proposal to back-calculate from a zero residue is the most promising approach I've seen suggested. Note that it would automatically concentrate our efforts on only those exponents that actually correspond to prime Mersennes!)

[cheesehead]

Originally Posted by davieddy

Is it not something of a remarkable coincidence that P-1 is so near the borderline of what is worthwhile before LL testing?

Yes ... one might speculate that an Intelligent Designer arranged it so!

- - -

For readers not familiar with how P-1 is done in GIMPS:

The B1/B2 bounds for P-1 are specifically chosen (via an algorithm designed by an intelligent human) so as to make the P-1 effort worthwhile compared to (a) the probability of finding a factor and (b) the amount of work required to perform the two, or one, L-L tests that would be eliminated by finding a factor in P-1.

- - -

George,

Has the P-1 bounds-choosing algorithm been tweaked to include the cost of the last 2 (or whatever) bit-levels of TF, if not yet done, as part of what would be saved if P-1 finds a factor?

[Prime95]

Originally Posted by cheesehead

... which differs qualitatively from what they might well have experienced with the v4 server, how?

With the v4 server the LL tester would not have to do 2 bits of TF.

We are "in danger" of having LL test time (which we need to maximize) "wasted" doing TF (where we have a surplus of capacity now).

Has the P-1 bounds-choosing algorithm been tweaked to include the cost of the last 2 (or whatever) bit-levels of TF, if not yet done, as part of what would be saved if P-1 finds a factor?

No. I expect it would have a negligible impact. In fact, it would probably choose smaller bounds. Not only am I not accounting for the TF saved, I am overcounting the LL time saved as some of that will not occur because TF of the last 2 bits will find some factors.