20120703, 22:45  #1365  
"James Heinrich"
May 2004
exNorthern Ontario
3^{2}×389 Posts 
Quote:
A stage2 savefile is also useful: * If B1new = B1old and B2new > B2old then stage2 will continue from B2old. * If B1new > B1old then stage1 will continue from B1old and stage2 will be redone from the start (same as if you only had a stage1 savefile). 

20120703, 22:59  #1366 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
16065_{8} Posts 
Doing stage 2 depends on the results from stage 1.
If you have a save file for B1o and B2o, if you want to increase B1o, then you will lose any stage 2 work you have done. This is why Prime95 ignores any new B1 with an old B2, because that would mean throwing out the previously done S2 work. You can always start any stage 2 bound from an arbitrary B1, if you have the save file for B1. Last fiddled with by Dubslow on 20120703 at 23:00 
20120704, 07:25  #1367 
Romulan Interpreter
Jun 2011
Thailand
2^{4}×13×47 Posts 
B2 does not matter. If you have old files saved at the end of the stage 1, then you can extend B1 (no matter what you do with B2, increase it or decrease it) and the work will be resumed from the old saved file.
Having B1new>B1old is always better, no matter how the relation between B2old and B2new. Stage 1 is the "certitude". Stage 2 is more or less a "lottery", finding the lucky number... Moreover, there must be a single lucky number, if there are two (between B1 and B2) the stage 2 will fail. This is like fishing, in stage 1 you start taking the water out from the lake. If during this process you catch a fish, is yours, and the job is finished. If not, you can return any time and take more water out from the lake, assuming the status/level of water is the same, it did not rain or someone put the water back (i.e. if you have the saved file). In stage 2, you can take a boat, chose your favorite fishing net and go fishing. You can use many nets in the same time, 2, 6, 30, or a full BrentSuyama set, but when you catch a fish, you must catch all his brothers in the same time, otherwise the brothers which are free will sink your boat. With these rules you may be lucky and find a fish with no brother (a single big factor of q1, or of** k, between B1 and B2), or you can catch a small family in the same time, if it is really small (like two brothers only, one brother is 6k1 and another is 6k+1 ) But generally you will come back emptyhanded, wet, and swimming.... Taking water out of the basin is easier, more certain, and... safe. **Comic note: for mersenne numbers this method should be called "q1" or "k" . No disrespect for Pollard, but we use p as the prime exponent, so if p is a prime, the factors which Mp might have, are usually denoted q. So, the method tries to find a factor q of Mp=2^p1, and it will succeed if all prime factors of q1 are small enough. Using "p1" here is confusing and wrong. OTOH, if q divides Mp, then q is always of the form q=2kp+1, so we are in fact looking for prime factors of 2kp, or more exact, factors F=f^{x} of k=(q1)/(2p)), with f prime and x natural. If all such factors F of k are under B1 (we say k is "B1powersmooth", or easier, just "smooth") then the "q1" method will always find the factor q of Mp in stage 1. Last fiddled with by LaurV on 20120704 at 07:29 
20120706, 17:39  #1368 
Dec 2003
Paisley Park & Neverland
5×37 Posts 
Questions, questions, questions.
Do we currently complete enough P1 per day?
Would it be a good idea to up the P1 bounds to search deeper? Or, on the other hand, to lower the bounds to complete (say) double the exponents at (say) only 20% less chance to find a factor? 
20120706, 17:57  #1369 
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{3}·17·73 Posts 
As of the last month or so, the GPU72 subproject has been completing about the same number of P1 runs as there are daily LL completions. This is addition to what people are doing directly from PrimeNet. (Note the graph shows a descending trend because many of our biggun P1ers submit their results in large batches every week to ten days.)
I'll let others who understand the cost/benefit of P1 work better than I do speak to this. 
20120706, 18:00  #1370 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
GPU to 72 alone does roughly as many P1 as LL tests completed per day. Combine that with the many P1 workers on PrimeNet who don't go through GPU272, I'm pretty sure P1 is keeping ahead of LL testers.
Even so, increasing bounds would not be a good idea; a lot of work has been put into getting the bounds selection to be as efficient as possible, meaning balancing finding a factor vs. how much effort could have been put into an LL test instead of P1 work. Increasing bounds may push P1 throughput to be roughly equal to LL throughput, but GIMPS would progress a bit slower for the same total amount of work. Edit: Whoops, cross post. Last fiddled with by Dubslow on 20120706 at 18:00 
20120706, 18:20  #1371 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{4}·3^{2}·53 Posts 
Some people feel that finding a factor is more satisfying than 2 matching LL tests. For those people, it makes sense to increase the P1 bounds even though it decreases GIMPS total throughput.

20120706, 18:38  #1372 
Dec 2003
Paisley Park & Neverland
5×37 Posts 
But wouldn't it be better (in the sense of personally finding as many factors as possible) to lower the bounds to find more factors per time as the chance to find a factor does not increase proportionally to the time spent?
But that leaves us with "incomplete" P1 before LL... andafterwards P1 cannot be taken to the next level as easy as TF. 
20120706, 18:42  #1373  
"James Heinrich"
May 2004
exNorthern Ontario
6655_{8} Posts 
Quote:


20120708, 15:02  #1374 
Sep 2002
2·401 Posts 
I think something strange has happened. I was looking up exponent M56412857 that my copy of Prime95 says found a factor a few hours ago. I used the http://mersennearies.sili.net/expon...ponentdetails= page to look it up. I noticed that the factor Prime95 says it found from my use was already listed, but not as a P1. I went ahead and manually submitted my result copying it from my result file and it mentioend something about "skipping the known factor" and now it's listed as mine. I wonder if someone should investigate this if it was already a known factor somehow.

20120708, 15:16  #1375 
Romulan Interpreter
Jun 2011
Thailand
2^{4}×13×47 Posts 
There is nothing wrong. The PrimeNet data base (to which P95 reports) is separate. When a factor is found, it does not say in the "exponent status" report who found the factor. The other data base (from James, to which you reported the factor) search the first data base on time basis and gets the factors that were reported meantime, but it can't guess who reported them and which method was used to find them. When you reported your factor you just clarified those aspects.
