[QUOTE=Dubslow;285854]I'm pretty sure I agree here, however the more I think about it, the more systematic inefficiencies I see, i.e. instead of trying to treat the symptoms like I originally suggested, lets see if we can do anything to stop these P-1s from appearing, or get them Stage 2 the first time somehow, or bladeeblabla.[/QUOTE]

Let's argue this from another angle...

Perhaps those who ask for LL work should only do LL work.

Let the P-1 work be left for those who understand what they're getting themselves into (knowing they won't find a MP with this method), and let those who get LL work assigned without P-1 done ("properly" or not) take the "exposure" of having a slightly lower chance of finding the next MP.

[QUOTE=axn;285690]All three of scenarios are trivially invalid. Prime95 has a working memory requirement of about 50MB. So merely running P95 will cause trashing.[/QUOTE]Let me clarify.

My three scenarios were each intended to have enough free memory so that prime95 could run without thrashing _unless_ it did P-1 stage 2. I thought that intent was obvious, but it wasn't. I should have explained the purpose of the figure instead of just throwing in the [strike]40MB[/strike] 50MB figure without explaining the intended significance it had for me.

I apologize for not recognizing earlier that that was the basis of your objection -- that I hadn't explained that the 40MB/50MB was not to be taken literally, but was intended to represent an amount in which prime95 could run without thrashing.

[I](However, I thought that this:[QUOTE=axn;285690]But I'll assume that there is a certain usage level at which Stage 2 will cause trashing, and it is this that you're interested in (not the specific number 40).[/QUOTE]indicated that you DID understand what I meant!!!!)[/I]

So, will you please answer the following reworded questions,
first with the assumption that the 90% allocation limit is NOT relevant, and
second, without that assumption
?

Suppose that [B]Xmb[/B] denotes the amount of memory in which prime95 can run LL, TF, P-1 stage 1, or P-1 stage 2 with "available memory" = no more than 8 MB, without causing any thrashing.

Scenario 1) Suppose a [U]minimum[/U] system has applications that use all but [B]Xmb[/B] of RAM without thrashing. Then Prime95 is introduced and, except for P-1 stage 2 with "available memory" > 8 MB, exists peacefully without causing any thrashing. But stage 2 with "available memory" > 8 MB does cause thrashing, noticeably slowing other applications. Is that acceptable, in your opinion?

Scenario 2) Suppose a [U]typical[/U] system has applications that use all but [B]Xmb[/B] of RAM without thrashing. Then Prime95 is introduced and, except for P-1 stage 2 with "available memory" > 8 MB, exists peacefully without causing any thrashing. But stage 2 with "available memory" > 8 MB does cause thrashing, noticeably slowing other applications. Is that acceptable, in your opinion?

Scenario 3) Suppose a [U]maximum[/U] system has applications that use all but [B]Xmb[/B] of RAM without thrashing. Then Prime95 is introduced and, except for P-1 stage 2 with "available memory" > 8 MB, exists peacefully without causing any thrashing. But stage 2 with "available memory" > 8 MB does cause thrashing, noticeably slowing other applications. Is that acceptable, in your opinion?

[QUOTE=Dubslow;285732]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.[/QUOTE]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 [I]are NOT simply like stage 1&2 runs without the stage 2[/I].

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.

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.

[url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=50007599[/url]

That's one of the best case scenarios, at around [url=http://www.wolframalpha.com/input/?i=3.0808%2F5.7492&t=crmtb01].54[/url] 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.

[QUOTE=Dubslow;285958]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.[/QUOTE]... while costing half or less of the P-1 time!!

Don't leave that out.

[quote]That's one of the best case scenarios, at around [URL="http://www.wolframalpha.com/input/?i=3.0808%2F5.7492&t=crmtb01"].54[/URL] times the usual chance of finding a factor. Most B1=B2 have a ratio lower than that.[/quote]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.

[quote]I've already stated my agreement that redoing these is not worth it at the moment and for the foreseeable future.[/quote]But do you understand the cost-benefit analysis of [I]why[/I] 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?

But the work done is [url=http://www.wolframalpha.com/input/?i=2.1383%2F3.3713&t=crmtb01]more than .54[/url]. Dividing the relative factor chance by relative work, we get a relative efficiency of [url=http://www.wolframalpha.com/input/?i=3.0808%2F5.7492*3.3713%2F2.1383&t=crmtb01].84[/url]. 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.

[QUOTE=Dubslow;285980]But the work done is [URL="http://www.wolframalpha.com/input/?i=2.1383%2F3.3713&t=crmtb01"]more than .54[/URL].[/QUOTE]

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.

- - - - -

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

- - - - -

[quote]Dividing the relative factor chance by relative work, we get a relative efficiency of [URL="http://www.wolframalpha.com/input/?i=3.0808%2F5.7492*3.3713%2F2.1383&t=crmtb01"].84[/URL]. 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'.[/quote]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 [I]IF there were actually a possibility to do stage 2 on the system in question[/I].

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

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. [U]There was no such choice for prime95 when it executed those runs -- it could do ONLY a stage 1-only run[/U].

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.

[quote]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.[/quote]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?)

[quote]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.[/quote]... 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.