mersenneforum.org > Data Thinking out loud about getting under 20M unfactored exponents
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2021-04-21, 16:09   #386
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

32·5·103 Posts

Quote:
 Originally Posted by chalsall Indeed. Thanks George! I don't have many human cycles at the moment, but I do have a few CPU cycles to burn... Could anyone give me an example of a P+1 worktodo line that would be appropriate for the <2K sub-sub-sub project?
From George's post:

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 P-1, the fact that factors of Mersenne numbers is 1 mod 2p is of no value.
Thus, P-1 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 P-1 stage 1
but several times faster than ECM stage 1.  P+1 stage 2 is a little faster than
P-1 stage 2 which in turn is a little faster than ECM stage 2.
Unlike P-1, 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 P-1, if how_far_factored is specified, prime95 will ignore B2 and calculate the
best B2 value for the given B1.
and:

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.

2021-04-21, 16:11   #387
chalsall
If I May

"Chris Halsall"
Sep 2002

2×4,787 Posts

Quote:
 Originally Posted by axn Ho many assignments and what range?
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:
 Originally Posted by axn Since this is brand new work type, nothing has been worked as of yet. But all reported results should show up under the exponent's history (in theory). I don't know if this information will be readily available anywhere else.
Yeah... I was more wondering about an example of an already completed run, so I know what my spiders need to make friends with.

I guess for this use case, we'll just coordinate here (or another sub-thread).

Thanks for your help getting an initial test batch defined.

2021-04-21, 16:16   #388
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

32·5·103 Posts

Quote:
 Originally Posted by chalsall Let's run the experiment in the 31.5M range.
At the present time -Anon- is TF'ing 31.5M.

2021-04-21, 16:21   #389
chalsall
If I May

"Chris Halsall"
Sep 2002

100101011001102 Posts

Quote:
 Originally Posted by petrw1 At the present time -Anon- is TF'ing 31.5M. Though he may pause if he reads this thread
I got the impression he had stopped at 75. But, good point; that range can be cleared by going to 76.

2021-04-21, 16:56   #390
axn

Jun 2003

2×3×827 Posts

The attached file has 153 assignments in the range 31.50-31.52, 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 have excluded those that have been TF'ed to 76 bits, as well as those that have been relatively poorly P-1'ed (the thinking being, those exponents might be better off being P-1'ed deeper rather than P+1).

I don't know what are optimal parameters, instead I have gone for a range of B1 values from 300k-600k. 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 P-1 done in the range and then picking equal or lesser values (since P+1 stage 1 is about half as fast as P-1).
Attached Files
 assignments.txt (5.5 KB, 7 views)

2021-04-21, 16:58   #391
axn

Jun 2003

496210 Posts

Quote:
 Originally Posted by chalsall I got the impression he had stopped at 75. But, good point; that range can be cleared by going to 76. axn, please give me 300# in 42.6M instead. Thanks.
Oops, didn't see it. Ok, I will whip up something in that range. But the 31.5 is still there if you need.

2021-04-21, 17:06   #392
axn

Jun 2003

2·3·827 Posts
42.6 range P+1 assignments

Ok. Take 2. Attached file has about 300 assignments in the 42.60-42.62. 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
If you can run these first five assignments and report back on B2 selection, run times (B1/B2 splits) and probabilities, we can then optimize the parameters for the rest of the runs.
Attached Files
 assignments.txt (10.9 KB, 4 views)

2021-04-21, 17:16   #393
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

3×11×227 Posts

Quote:
 Originally Posted by petrw1 George: Your posts talks about choosing B1 based on the current ECM B1. For my case do you have any recommendations for P+1 for choosing B1 based on how much P-1 has already been done? I am tempted to assume that P+1 will find different factors than P-1 which makes me hopeful even smallish B1/B2 will have reasonable success? Am I totally out to lunch?
We're learning about best bounds selection together.

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 P-1, but is vastly inferior to P-1. 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 100-300 P+1 runs to find a single factor.

I fear that for exponents above 20M you're better off extending P-1 bounds rather than doing P+1. As you gather data, you may prove my fear wrong.

2021-04-21, 17:23   #394
chalsall
If I May

"Chris Halsall"
Sep 2002

2×4,787 Posts

Quote:
 Originally Posted by axn If you can run these first five assignments and report back on B2 selection, run times (B1/B2 splits) and probabilities, we can then optimize the parameters for the rest of the runs.
OK. Thanks a lot! The first five are running now.

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] 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 AVX-512 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.

 2021-04-21, 17:24 #395 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 11101010000112 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 P-1 has been done on almost all "small" exponents. For the PRP-CF 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.
2021-04-21, 17:26   #396
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

11101010000112 Posts

Quote:
 Originally Posted by chalsall Seems like there's still some Primenet work to do though...
Primenet accepts P+1 results, but does not recognize/coordinate P+1 assignments.

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