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
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