P-1 Question

[cheesehead]

Originally Posted by Dubslow

As for this argument (still relatively unrelated to the OP) IMO, if a computer is doing nothing but Stage 1 P-1 without Stage 2, and is contributing nothing else to GIMPS, I think GIMPS would be better if that computer didn't participate at all. Beggars can't be choosers, but if someone gives the beggar a rotten piece of vegetables, he will throw it out.

Are you aware of this: Given two systems, identical except that one of them has the "available memory" default value of 8 MB, and the other has specified "available memory" = 300 MB (for instance), the bounds-choosing algorithm will choose a significantly high B1(=B2, thus stage 1 only) for the first than it will for the second. For instance, the first system might have B1=B2=500000 and the second system have B1=375000,B2=6750000.

The point is that on systems that had bounds chosen by the prime95 bounds-choosing algorithm, stage 1-only runs are NOT simply like stage 1&2 runs without the stage 2.

Example from the factoring limits report:

50007499 69 560000 9660000
50007599 69 805000 805000

The stage 1-only run for exponent 50007599 went to a considerably higher B1 than the stage 1&2 run for 50007499.

GIMPS would not have been better-off for that particular system not to do a stage 1-only P-1. It spent the amount of time doing P-1 so that

(its chance of finding a factor) * (the time needed for it to do an L-L) was maximally better than (the time it spent doing the P-1),

that is, that its time spent on P-1 saved GIMPS at least that much on L-L tests (on average over many instances)

That's the same criterion by which the bounds-choosing algorithm judges what B1 and B2 to use for a stage 1&2 run.

[Dubslow]

I am well aware of those things; however even extended B1 runs (750K instead of 500K+12M) still have half or less the chance on finding a factor.

http://mersenne-aries.sili.net/expon...tails=50007599

That's one of the best case scenarios, at around .54 times the usual chance of finding a factor. Most B1=B2 have a ratio lower than that.

I've already stated my agreement that redoing these is not worth it at the moment and for the foreseeable future.

[cheesehead]

Originally Posted by Dubslow

I am well aware of those things; however even extended B1 runs (750K instead of 500K+12M) still have half or less the chance on finding a factor.

... while costing half or less of the P-1 time!!

Don't leave that out.

That's one of the best case scenarios, at around .54 times the usual chance of finding a factor. Most B1=B2 have a ratio lower than that.

But that .54 isn't the whole story. For proper analysis, one needs to combine that with the relative amounts of time (as I did in post #13).

If case B has .54 as much chance of finding a factor as case A, but case B takes only .49 as much time as case A, then case B is a more efficient use of time for GIMPS.

If 1000 runs of case A find 100 factors in 1000 units of time, but 1000 runs of case B find 54 factors in 490 units of time, then case B is better for GIMPS. 2000 runs of case B would find 108 factors (more than case A), but use only 980 units of time (less than case A), a better ratio.

I've already stated my agreement that redoing these is not worth it at the moment and for the foreseeable future.

But do you understand the cost-benefit analysis of why the redoing is not worth it -- or, more accurately, why there are other tasks that would bring GIMPS more benefit for the same amount of time expended?

[Dubslow]

But the work done is more than .54. Dividing the relative factor chance by relative work, we get a relative efficiency of .84. Not only is total factor chance less, but factor chance per work done is also less. It is the combination of these I declare 'half-assed'.

The cost-benefit analysis is very simple: we get less benefit (reduced factor chance on B2 redo) for equal cost (standard P-1 cost) than 'normal' P-1, which with same cost, has higher factor chance.

That said, that does not mean that redoing B1=B2 (or other poor P-1 runs, as James' site locates) is not beneficial, only that it is less beneficial than a 'fresh' P-1.

[cheesehead]

Originally Posted by Dubslow

But the work done is more than .54.

You are correct!

Sorry about that. I was Posting When Tired.

I see now that I should have doubted that my example (with less GHz-days work) was realistic, and double-checked elsewhere.

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*** => I hereby renounce my post #102 above -- it contains multiple mistakes. <= ***

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Dividing the relative factor chance by relative work, we get a relative efficiency of .84. Not only is total factor chance less, but factor chance per work done is also less. It is the combination of these I declare 'half-assed'.

But you persist in making that invalid value judgement because you keep ignoring what I've pointed out about the context of those stage 1-only P-1 runs!

Comparing the stage 1-only figures to the stage 1&2 figures would be valid (and thus you could justify your value judgement) only IF there were actually a possibility to do stage 2 on the system in question.

But when the bounds-choosing algorithm chose B1=B2 in those past cases, it was only because stage 2 was not possible because "available memory" was insufficient!!!

As I've already tried to explain to you in earlier posts, in the ACTUAL, REAL-LIFE situations of those past stage 1-only runs prime95 did NOT have a choice between stage 1-only or stage 1&2 -- which is the choice you keep assuming was available when you make the "half-assed" value judgement. There was no such choice for prime95 when it executed those runs -- it could do ONLY a stage 1-only run.

Please stop denigrating past work for which the choice made was the GIMPS-optimum choice that was actually available at the time the choice was made.

The cost-benefit analysis is very simple: we get less benefit (reduced factor chance on B2 redo) for equal cost (standard P-1 cost) than 'normal' P-1, which with same cost, has higher factor chance.

1) That statement needs to explicitly mention "stage 1-only" or "stage 1&2" so that the reader can figure out what you mean.

2) What are your definitions of "standard" and "normal" for that statement, and "fresh" in your following statement? (Shall I suggest some alternatives using terms that are more customary when discussing P-1, so you could decide which was what you meant?)

That said, that does not mean that redoing B1=B2 (or other poor P-1 runs, as James' site locates) is not beneficial, only that it is less beneficial than a 'fresh' P-1.

... and generally less beneficial than some other types of work the systems could actually be doing now, instead, for GIMPS.

Saying that redoing (I prefer "extending") the old stage 1-only runs is less beneficial than doing a stage 1&2 originally isn't helpful to us now because we don't actually have the choice of doing stage 1&2 in the original P-1 run -- it's in the past.

It's more helpful to compare the benefits of actual choices that we really have available to us now than to do a comparison to an imaginary choice we don't have.