On Saturday 23 November 2002 02:41, Torben Schlüntz wrote: > [... snip ...] > Sorry Nathan. It is my fault you read the IMHO paragraph in a wrong > way. I meant I had that point of view UNTIL I discussed it...... As > George argue: Nobody would do LL if a succesful TF was rewarded the > same - he is truly right.
>From the point of view of the project, the objective is to find Mersenne primes. Finding factors, like completing LL tests returning a non-zero residual, only eliminates candidates. However, from the point of view of league tables, it seems to make sense to award effort expended (in good faith); otherwise there would be only two raks in the table: those who have found a prime, and those who haven't! > My goal is to get the succesful TF rewarded a bit higher. As it is now > someone might skip the 57-65 range and only do the 66-bit part, thus > missing factors and get fully rewarded for only doing half the work. This is not a particularly effective cheat; you still end up having to do significantly more than half of the computational work. Is there any evidence that this may be happening? Does it make sense to impose a "penalty clause" i.e. if someone subsequently finds a factor in a range you claim to have sieved, you lose 10 times the credit you got for the assignment? N.B. There will be _occasional_ instances where an "honest" user misses a factor, possibly due to a program bug, possibly due to a hardware glitch. > [... snip ...] > Composite exponents was removed long before the project. Lucas must have > known the exponent needed to be prime. I believe a Mersenne number has > to have an exponent which is a positive integer?! The exponents above > 79.300.000 are still candidates, though George has chosen to limit his > program to this size and I think with very good reason. Hmm. As it happens, one of my systems has just completed a double-check on exponent 67108763. This took just over a year on an Athlon XP1700 (well, actually it was started on a T'bird 1200). The fastest P4 system available today could have completed the run in ~3 months. The point is that running LL tests on exponents up to ~80 million is easily within the range of current hardware. Personally I feel it is not sensible to expend much effort on extremely large exponents whilst there is so much work remaining to do on smaller ones. I justify running the DC on 67108763 as part of the QA effort. > > BTW, the list of found factors contains 2.500.000+ but the "top > producers list" only contains 30.000- of these. GIMPS must be > responsible for far more than only 30.000 factors. Any explanation for > that? Well, there are a lot of factors which can be found by algebraic methods rather than by direct computation: e.g. if p+1 is evenly divisible by 4, and p and 2p+1 are both prime, then 2^p-1 is divisible by 2p+1. Also, there are more efficient methods of finding _small_ factors (up to ~2^48) than individually sieving for each exponent. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers