20210421, 16:09  #386  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3^{2}·5·103 Posts 
Quote:
Code:
P+1 factoring. A worktodo.txt entry looks like this: Pplus1=k,b,n,c,B1,B2,nth_run[,how_far_factored][,"known_factors"] Unlike P1, the fact that factors of Mersenne numbers is 1 mod 2p is of no value. Thus, P1 is vastly more effective at finding factors. A P+1 run is about as valuable as running one ECM curve. P+1 stage 1 is 50% slower than P1 stage 1 but several times faster than ECM stage 1. P+1 stage 2 is a little faster than P1 stage 2 which in turn is a little faster than ECM stage 2. Unlike P1, P+1 has only a 50% chance of finding a factor if factor+1 is B1/B2 smooth. Thus, it makes sense to do 1 or 2 (maybe 3) runs. That is what the nth_run argument is for. There are two special starting values for P+1 that have a slightly higher chance of finding a factor. These special starting values correspond to nth_run=1 and nth_run=2. Like P1, if how_far_factored is specified, prime95 will ignore B2 and calculate the best B2 value for the given B1. Code:
My thoughts are to choose B1 well above the current B1's being handed out by the server for ECM. For the few exponents I tried in the 4.7M area, ECM is presently being done at B1=50K, I chose P+1 with B1=1M. 

20210421, 16:11  #387  
If I May
"Chris Halsall"
Sep 2002
Barbados
2×4,787 Posts 
Let's run the experiment in the 31.5M range. If you could give me let's say 300# assignments so we get a reasonable sample set. Please make them reasonably aggressive (read: good probability of a positive, but not stupidly expensive).
Quote:
I guess for this use case, we'll just coordinate here (or another subthread). Thanks for your help getting an initial test batch defined. 

20210421, 16:16  #388 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3^{2}·5·103 Posts 

20210421, 16:21  #389 
If I May
"Chris Halsall"
Sep 2002
Barbados
10010101100110_{2} Posts 

20210421, 16:56  #390 
Jun 2003
2×3×827 Posts 
The attached file has 153 assignments in the range 31.5031.52, the first four of which are:
Code:
Pplus1=1,2,31500281,1,300000,0,1,75 Pplus1=1,2,31500361,1,400000,0,1,75 Pplus1=1,2,31500457,1,500000,0,1,75 Pplus1=1,2,31500767,1,600000,0,1,75 I don't know what are optimal parameters, instead I have gone for a range of B1 values from 300k600k. I am also relying on P95 to compute optimal B2, hence B2 is set as 0. If you can run these first four assignment and report back on B2 selection, run times (B1/B2 splits) and probabilities, we can then pick the optimal parameters. Choice of B1 was based on looking at the current state of P1 done in the range and then picking equal or lesser values (since P+1 stage 1 is about half as fast as P1). 
20210421, 16:58  #391 
Jun 2003
4962_{10} Posts 

20210421, 17:06  #392 
Jun 2003
2·3·827 Posts 
42.6 range P+1 assignments
Ok. Take 2. Attached file has about 300 assignments in the 42.6042.62. First five are:
Code:
Pplus1=1,2,42600139,1,400000,0,1,75 Pplus1=1,2,42600221,1,500000,0,1,75 Pplus1=1,2,42600289,1,600000,0,1,75 Pplus1=1,2,42600367,1,700000,0,1,75 Pplus1=1,2,42600379,1,800000,0,1,75 
20210421, 17:16  #393  
P90 years forever!
Aug 2002
Yeehaw, FL
3×11×227 Posts 
Quote:
I suggest picking one exponent and try a B1/B2 combination  plus specify the TF bit level. Start prime95 and it will tell you the chance of finding a factor. Abort, select different B1/B2, run prime95 and look at the chance of finding a factor. Repeat until you have a decent idea as to how bounds correlate with probability. Choose B2 somewhere between 20 and 80 times B1. Are you out to lunch? Somewhat. P+1 will find different factors than P1, but is vastly inferior to P1. The loss of the "free 2*p" in B1/B2 smoothness for Mersenne numbers where factors are known to be of the form 2*k*p+1 is huge. Add on to that the 50% chance that P+1 won't find the factor even if it is B1/B2 smooth. Depending on TF levels, you're probably looking at 100300 P+1 runs to find a single factor. I fear that for exponents above 20M you're better off extending P1 bounds rather than doing P+1. As you gather data, you may prove my fear wrong. 

20210421, 17:23  #394  
If I May
"Chris Halsall"
Sep 2002
Barbados
2×4,787 Posts 
Quote:
Seems like there's still some Primenet work to do though... Code:
[Main thread Apr 21 17:19] Mersenne number primality test program version 30.6 [Main thread Apr 21 17:19] Optimizing for CPU architecture: Core i3/i5/i7, L2 cache size: 4x1 MB, L3 cache size: 33 MB [Main thread Apr 21 17:19] Starting worker. [Comm thread Apr 21 17:19] Registering assignment: P+1 M42600221 [Comm thread Apr 21 17:19] PrimeNet error 44: Invalid assignment type [Comm thread Apr 21 17:19] ra: unsupported assignment work type: 6 [Work thread Apr 21 17:19] Worker starting [Work thread Apr 21 17:19] Setting affinity to run worker on CPU core #1 [Work thread Apr 21 17:19] [Work thread Apr 21 17:19] P+1 on M42600221 with B1=500000, B2=TBD [Work thread Apr 21 17:19] Setting affinity to run helper thread 2 on CPU core #3 [Work thread Apr 21 17:19] Using AVX512 FFT length 2240K, Pass1=128, Pass2=17920, clm=4, 4 threads [Work thread Apr 21 17:19] Setting affinity to run helper thread 3 on CPU core #4 [Work thread Apr 21 17:19] Setting affinity to run helper thread 1 on CPU core #2 [Comm thread Apr 21 17:19] Done communicating with server. [Work thread Apr 21 17:20] M42600221 stage 1 is 0.78% complete. Time: 35.714 sec. [Work thread Apr 21 17:20] M42600221 stage 1 is 1.71% complete. Time: 35.840 sec. [Work thread Apr 21 17:21] M42600221 stage 1 is 2.63% complete. Time: 36.335 sec. 

20210421, 17:24  #395 
P90 years forever!
Aug 2002
Yeehaw, FL
1110101000011_{2} Posts 
We do know that P+1 is better than ECM  roughly the same chance of success but several times faster.
We do know that TF becomes more and more expensive the smaller the exponent. We also know that deep P1 has been done on almost all "small" exponents. For the PRPCF and this 20M project, a coordinated P+1 attack on exponents below say 5 or 10 million should be worthwhile. It might be nice to start a new thread to do the coordination and reach a consensus on the target B1 for the various exponent ranges. 
20210421, 17:26  #396 
P90 years forever!
Aug 2002
Yeehaw, FL
1110101000011_{2} Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Thinking of Joining GPU to 72  jschwar313  GPU to 72  3  20160131 00:50 
Thinking about lasieve5  Batalov  Factoring  6  20111227 22:40 
Thinking about buying a panda  jasong  jasong  1  20081111 09:43 
Loud thinking on irregular primes  devarajkandadai  Math  4  20070725 03:01 
Question on unfactored numbers...  WraithX  GMPECM  1  20060319 22:16 