20210511, 17:38  #100 
P90 years forever!
Aug 2002
Yeehaw, FL
7533_{10} Posts 

20210515, 15:43  #101  
Jul 2003
wear a mask
2^{2}·419 Posts 
Quote:
Here's a thought experiment: I picked a somewhat arbitrary time of 15 weeks to spend on P+1 tests with a CPU farm. That 15 weeks translates to 3.5 hours per remaining exponent. In 3.5 hours, a representative CPU can do 1 test with B1 = 2400K or 2 tests with B1 = 1270K or 3 tests with B1 = 900K. The 1 large test will have probability 1.14% to find a factor. The expected number of factors over the 1850 remaining exponents will be 21.1. The 2 medium tests (with seeds nth_run=1,2) will have probabilities 0.822% and 0.387% (sum 1.21%); the expected number of factors will be 22.4. The three small tests will have probabilities 0.68%, 0.317% and 0.0713% (sum 1.07%); the expected number of factors will be 19.8. If I want to optimize factors found per time spent, I will choose two runs with seeds nth_run = 1,2. There's not a lot of difference in the expected numbers above, but extending that logic to a larger range, the benefits become clear. This is probably the correct strategy for many generic factoring efforts. Good, general advice might be to run one P1 curve, and then two P+1 curves before starting ECM efforts on an exponent. However, that approach is not directly compatible with the goal of getting less than 2000 unfactored exponents in the 14.0M range. For that goal, it seems wiser to spend 15 weeks running 1 large P+1 test on each exponent using nth_run = 1. Then, I expect to find about 20 factors. Depending on how close we are to the goal of 2000, it may or may not make sense to run for another 15 weeks to find approximately 10 factors with the second seed. Last fiddled with by masser on 20210515 at 15:46 

20210525, 21:28  #102  
Jul 2020
24_{10} Posts 
Quote:
In total, I did 294 P+1 tests and 231 P1 tests. Out of them, four P1 tests were successful (506047, 505313, 504377, 503453) and one P+1 test (505877). 

20210526, 00:21  #103 
P90 years forever!
Aug 2002
Yeehaw, FL
3^{5}·31 Posts 

20210529, 14:55  #104 
Romulan Interpreter
Jun 2011
Thailand
7^{2}·197 Posts 
Question: if I want to waste a couple of cycles to run P+1 in 1.7M to 2M, what conservative/reasonable/aggressive B1 and B2 limits should I use? (and does it make any sense? or there was too much ECM already done there?)
Last fiddled with by LaurV on 20210529 at 15:40 
20210529, 15:17  #105 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
265A_{16} Posts 

20210529, 15:57  #106  
Jul 2003
wear a mask
1676_{10} Posts 
Quote:
I seem to recall very old (yahoo groups days) discussions of a ruleofthumb, that as you progressed in factoring effort, P1 B1 was 10x the ECM level; P+1 was somewhere in between. So, find the level and ECM B1, run P1 at B1 = 10xB1_ecm, then (perhaps multiple) P+1 with (25)xB1_ecm, then complete the ECM curves, then increment the level and iterate. This seems to line up with observations on this forum, but the local strategy is still workinprogress. So, given all that, I think a "reasonable" B1 for P+1 in the 1.7M to 2M range would be B1=1M. "Aggressive" might be B1=5M. "Low probability, but fast" might be B1<500K. Also, you can see here what has been successful in that range. For B2, just let prime95/mprime decide, using the known TF level (maybe artificially increased to reflect completed ECM). Does it make sense? Certainly if you run the first P+1 curve on an exponent with decent bounds, there's a reasonable chance you'll find a factor that P1 couldn't find. Secondly, you'll be doing the various factoring efforts a favor, by settling the question of a hidden, easily found P+1 factor that has been missed by ecm and that P1 might never find. Very satisfying for the "completionists" working on Mersenne factoring . Last fiddled with by masser on 20210529 at 16:03 

20210529, 16:22  #107 
Jul 2003
wear a mask
1676_{10} Posts 
Here you go:

20210530, 03:44  #108 
Romulan Interpreter
Jun 2011
Thailand
7^{2}·197 Posts 

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