LL Test Rates and GIMPS Promotion
 

It seems that for a while now the ratio of first time LL tests to DCs has been about 2. I was wondering if there were any concern about the DCs falling away from the first time tests? Perhaps there could be a DC push like TPR did with their DC gauntlet, with the board members and such.

It also seems as though the completion rates are steadily increasing despite the increase in exponent values. I was also wondering if there would be any formal push to promote GIMPS, perhaps when the new server is online or sooner? I think a great resouce could be CS and Math departments at Universities, as well as primary schools which could use the hunt to promote math in general. Any ideas to promote the search?

Where's da :banana:

Re: LL Test Rates and GIMPS Promotion
 

[quote="Primenut"]It seems that for a while now the ratio of first time LL tests to DCs has been about 2. I was wondering if there were any concern about the DCs falling away from the first time tests?[/quote]
Why be concerned? There's no deadline, and we have an infinitude of Mnumbers yet to test. :)

[quote]Perhaps there could be a DC push like TPR did with their DC gauntlet, with the board members and such.[/quote]
You're free to start one if you wish.

But DC completions will speed up slightly a few months from now, anyway. Why? Because then DC assignments will reach the range (~10M) where first-time L-L assignments were when Prime95 introduced automatic pre-LL P-1 factoring. Right now, many DC assignments are for exponents that haven't had any P-1 performed, so the DCers perform P-1 in those cases before starting the DC L-L test. Once DC assignments reach the range where almost all exponents have already had P-1 performed, DCers won't be doing the P-1s before their L-Ls.

[quote]It also seems as though the completion rates are steadily increasing despite the increase in exponent values.[/quote]
Doesn't that mean that progress is already accelerating?

[quote]Once DC assignments reach the range where almost all exponents have already had P-1 performed, DCers won't be doing the P-1s before their L-Ls.[/quote]

Won't Prime95 still go ahead and do P-1 on the exponent anyway? I don't think the information about how much P-1 has been done gets included in the DC assignment.

[quote="geoff"]Won't Prime95 still go ahead and do P-1 on the exponent anyway? I don't think the information about how much P-1 has been done gets included in the DC assignment.[/quote]

That information isn't included, but all the client cares about is whether any P-1 has been done at all. If any has been done, the client doesn't do it again.

In the DC assignment line

DoubleCheck=eeeeeeee,bb,w

the w field is "0" if no P-1 has yet been done, or "1" if there has been P-1 performed (no matter what the B1/B2 limits).

Re: LL Test Rates and GIMPS Promotion
 

That gauntlet had nothing to do with accelerating DC production. I organized it and the reason was based solely on completion times. We needed to run stats, which were much easier to calculate by exponent rather than having to track progress within a test.

The total exponents used in the contest was 1000 and we didn't finish them all in that period. Some of the corporate farms operated on auto pilot and as such didn't draw from the pool.

An interesting side observation was that the mass factoring we did to prepare the pool prior to competing led to the discovery of a large number of factors. I did a run of 100 P-1 tests (160 MB ram allocated) and found 5 factors.

Of course, some team interested in boosting DC production could always challenge us to a gauntlet - but they have to visit our home to do that :banana:

[quote="Primenut"] Perhaps there could be a DC push like TPR did with their DC gauntlet, with the board members and such.

[/quote]

P-1 Factoring before double checking
 

Wouldn't GIMPS be better off if double checkers took into account the highest B2 that was ever done on a given exponent? That way, if more memory could be used in the P-1 test, perhaps a factor could be found that wouldn't be otherwise.

For instance, if the original tester only used 64 MB of RAM to do P-1 testing, and, 2 years later, the double checker has 512 MB of RAM, shouldn't that massive amount of RAM be used for P-1 testing *despite* the fact that P-1 has already been done? In other words, not all P-1 tests are equal...

Perhaps, P-1 testing should be distributed as completely separate assignments to those computers able to use massive amounts of memory. I'm sure a lot of low-memory P-1 tests get performed, and if this system were implemented, a lot of Lucas-Lehmer tests could be avoided. This would undoubtedly speed up the GIMPS project to some extent.

Given that P-1 testing increases GIMPS throughput by only 1% even with the most efficient P-1 bounds, I don't think there's much more squeezable out of it, especially considering that only one LL test is saved by P-1 at the DC stage.

P-1 factoring
 

No, I'm suggesting that P-1 be done once, after trial factoring, but before the first LL test, and when the P-1 factoring is assigned, it should only be assigned to computers with high amounts of memory. If a factor is found, then two LL tests are saved. Perhaps with this implementation, more than 1% of LL tests would be avoided. By the way, where did you get that statistic? The statistic for my team is that 3.2% of all LL assignments ended in a P-1 factor before the LL testing began. And not many of the computers on my team have high amounts of memory dedicated to Prime95...

I'd imagine if all P-1 factoring was done on computers with over a gigabyte of RAM, many more such factors could be found, and though it might not make a *huge* difference, it would help, wouldn't it?

Out of curiousity, are most P-1 factors found in stage one or stage two?

In my experience, stage one...

Re: P-1 factoring
 

[quote="trif"]increases GIMPS throughput by only 1%[/quote]

[quote="jobhoti"]3.2% of all LL assignments ended in a P-1 factor before the LL testing began. [/quote]

Both statements can be true. If the cost of a P-1 test is 2.2% of a double-check LL test time, then GIMPS throughput increases 3.2% - 2.2% = 1%

Re: P-1 Factoring before double checking
 

[quote="jobhoti"]Wouldn't GIMPS be better off if double checkers took into account the highest B2 that was ever done on a given exponent? That way, if more memory could be used in the P-1 test, perhaps a factor could be found that wouldn't be otherwise.[/quote]
The catch is that the probability of finding a factor with P-1 falls off relentlessly after a certain point, making it less efficient to prove a Mnumber composite by searching for a factor with P-1 than by running a DC L-L.

I.e. -- yes, it could be done, but it might not be worth it [i]from the standpoint of GIMPS throughput for its primary goal of determining the primality of Mersenne numbers[/i].

[quote]For instance, if the original tester only used 64 MB of RAM to do P-1 testing, and, 2 years later, the double checker has 512 MB of RAM, shouldn't that massive amount of RAM be used for P-1 testing *despite* the fact that P-1 has already been done? In other words, not all P-1 tests are equal...[/quote]
Correct. But the most valuable one is usually the first one, even if it had been done to only modest limits.

If someone has P-1ed with B1=125000, B2=1875000, for example, then if you are going to test to higher limits, say B1=350000,7000000, unless you have a save file from that first run your run will have to repeat all the computations that got the first stage 1 up to 125000 before you have any chance at all of finding a factor with your computations. That makes your run [b]much[/b] less efficient than if yours were the first run.

[quote]Perhaps, P-1 testing should be distributed as completely separate assignments to those computers able to use massive amounts of memory.[/quote]
Good idea. It's already been suggested that the PrimeNet server add a new class of assignments for P-1 factoring alone.

[quote]I'm sure a lot of low-memory P-1 tests get performed, and if this system were implemented, a lot of Lucas-Lehmer tests could be avoided. This would undoubtedly speed up the GIMPS project to some extent.[/quote]
But that depends on (1) whether the tradeoff between time to make the P-1 run and probability of finding a factor via that method is deemed worthwhile, and (2) whether the value of finding a specific factor is considered greater than the value of simply proving that a Mnumber is composite.

Is there any sort of promotional package that describes the work of GIMPS, its goals, the study touting its unobtrusiveness, a letter from George its founder, the rewards of contributing to math history, the uselessness of idle cycles etc.? Perhaps something that could be presented to ones employer or university especially to the IT people or science guys who have say-so over computer labs?

[quote="cheesehead"]
But DC completions will speed up slightly a few months from now, anyway. Why? Because then DC assignments will reach the range (~10M) where first-time L-L assignments were when Prime95 introduced automatic pre-LL P-1 factoring. Right now, many DC assignments are for exponents that haven't had any P-1 performed, so the DCers perform P-1 in those cases before starting the DC L-L test. Once DC assignments reach the range where almost all exponents have already had P-1 performed, DCers won't be doing the P-1s before their L-Ls.
[/quote]
Wouldn't the DC's slow down instead? Since there will be no more factors to find, there will be no more L-L tests to avoid. The whole point of the P-1 test (from GIMPS's point of view) is to [i]increase[/i] the average throughput of the L-L tests.

[quote="patrik"][quote="cheesehead"]
But DC completions will speed up slightly a few months from now, anyway. Why? Because then DC assignments will reach the range (~10M) where first-time L-L assignments were when Prime95 introduced automatic pre-LL P-1 factoring. Right now, many DC assignments are for exponents that haven't had any P-1 performed, so the DCers perform P-1 in those cases before starting the DC L-L test. Once DC assignments reach the range where almost all exponents have already had P-1 performed, DCers won't be doing the P-1s before their L-Ls.
[/quote]
Wouldn't the DC's slow down instead? Since there will be no more factors to find, there will be no more L-L tests to avoid. The whole point of the P-1 test (from GIMPS's point of view) is to [i]increase[/i] the average throughput of the L-L tests.[/quote]

Yes, but there will be fewer tests in each range because those with P-1 factors will have been eliminated and won't be handed out. So the cost of doing P-1 on those is saved in the DC phase.