LL Test Rates and GIMPS Promotion

[cheesehead]

Originally Posted by 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.

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 from the standpoint of GIMPS throughput for its primary goal of determining the primality of Mersenne numbers.

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...

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 much less efficient than if yours were the first run.

Perhaps, P-1 testing should be distributed as completely separate assignments to those computers able to use massive amounts of memory.

Good idea. It's already been suggested that the PrimeNet server add a new class of assignments for P-1 factoring alone.

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.

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.

[Primenut]

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?

[patrik]

Originally Posted by 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.

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 increase the average throughput of the L-L tests.

[trif]

Originally Posted by patrik

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 increase the average throughput of the L-L tests.

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.