View Single Post
Old 2003-07-11, 18:57   #6
Thomas11's Avatar
Feb 2003

78016 Posts
Default Some thoughts about future work and other things ...

Within about two months our project has found the amazing number of 160+ titanic primes. :D
Thanks to all of you! Great work!

There are a lot of things and problems which arise, when a project like ours is growing and gets "dynamical". So here are some thoughts, comments and ideas I have:

Actually Shane and me are sieving the list of possible 15k's up to 4.3 billion (2^32), which is the upper limit for LLR (it will run about 3 times slower on larger 15k's). From that sieving we will get a lot of "heavy-weighted" candidates, waiting to be tested by all of us. The computed weights give you an idea on the number of primes you may expect, e.g. a 15k with a larger weight may produce more primes than a 15k having a smaller weight. But there's no guarantee that the largest weight will give the most primes!
For example: The most frequent 15k up to now is 16995 for which we have found 10 primes for 110000<n<175000. But the weight for this candidate is only 3.08 (Nash weight = 5411). This is a quite low weight compared to our actual "almost"-4.0 candidates. Well, I haven't found any new primes for 15k=16995 in the range 175000<n<230000! This balances that low weight ...
You see, for finding many primes there is also a bit of luck needed. :?

Another thing is that some 15k's may be already tested by other people (non-group members). We try to check the candidates before we present them on our list. But we're all humans and therfore not free of errors. So please have yourself a look at Chris Caldwell's database and check the specific candidates you want to test, to avoid wasting you cpu power! (There may also be some really bad guys who take our list and test the candidates before we do - without beeing a member of our group ... :( any ideas on that topic?)

Those of you thinking about re-reserving 15k's which were already tested by someone else should contact that group member. May be he or she has sieved that 15k up to much higher n but didn't have tested the whole range for primality, e.g. in most cases I use NewPGen to sieve for n up to 200000, but sometimes (when there are not so many primes) I stop LLR around n = 160000 or so.

The last topic is on the speed of P4 vs. Athlon machines. I've found (and many others before me too) that NewPGen runs faster on Athlon's, while LLR is faster on the P4. Those of us, who have both types of machines available (I'm such a lucky guy :D) could run NewPGen on the Athlon and LLR on the P4. We could also think about splitting the sieving/LLRing between different people - those with an Athlon run NewPGen, those having a P4 run LLR. But then both should get credit on the primes found and therefore should have one common prover code. When we have found some "best" 15k's and decide to test for larger ranges of n we should think about some coordinated sieving (yes, to be done by those Athlon guys).

Comments and other ideas are welcome,
Thomas R.
Thomas11 is offline