mersenneforum.org > Data Thinking out loud about getting under 20M unfactored exponents
 Register FAQ Search Today's Posts Mark Forums Read

2021-04-22, 00:19   #419
James Heinrich

"James Heinrich"
May 2004
ex-Northern Ontario

25×3×5×7 Posts

Quote:
 Originally Posted by chalsall You'll now have to do a cost/benefit analysis to determine where the economic cross-over points are between ECM, deep TF'ing, deep P-1'ing, and this new P+1!!! As a function of 0.1M range, please...
Easily done. P+1 has never found a Mersenne factor, therefore optimal effort to spend on it is zero.

2021-04-22, 00:47   #420
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

121B16 Posts

Quote:
 Originally Posted by chalsall OK... Here are the log entries from my fastest machine for those who understand the maths behind all this. The probability percentage is indeed low... This is for 42600139. Code: [Work thread Apr 21 14:13] With trial factoring done to 2^75, optimal B2 is 42*B1 = 16800000. [Work thread Apr 21 14:13] Chance of a new factor assuming no ECM has been done is 0.274% [Comm thread Apr 21 14:48] Sending result to server: UID: wabbit/rdt1, M42600139 completed P+1, B1=400000, B2=16800000, Wi8: 4F3C1C20
If I have the gozintas correct then if you do all 2050 42.6M exponents with these bounds you should find 5 or 6 factors for 6,731 GhzDays. About 1,200 per factor.

There are only about 600 exponents left that I could still reasonably P-1 with aggressive bounds for an expected success rate of about 1.5% (9 factors) for about 5,000 GhzDays; about 550 per factor.
After that P-1 becomes very expensive with the success rate dropping to about 0.5%; and 1,700+ GhzDays per factor.

Comparatively to find the remaining 47 factors via TF would take about 800,000 GhzDays.

So...the only actual comparison I can do is from my own farm:

Option 1: If I do all the remaining with TF it would take 170 days for my 2080Ti.

Option 2: If I first complete the above 600 P-1 assignments that would take about 18 days on my 20 cores (5 PCs). 290 GhzDays/Day
I then TF for the remaining 38 factors in 109 days.
Option 2 total is 127 days.

Option 3: If I complete the P-1 in 18 days.
Then I do the P+1 (6,731 GhzDays) that is another 23 days.
Now if I do find 15 factors by P+/-1 the remaining 32 TF factors would take about 400,000 GhzDays or 85 calendar days.
The total in option 2 is 126 days.

So personally the P+1 benefit seems minimal.

However, if my farm had less CPUs or conversely if I had a 1080Ti instead of a 2080Ti the bottom lines would be quite different.

Does anyone see it different?

2021-04-22, 02:31   #421
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

112558 Posts

Quote:
 Originally Posted by petrw1 Does anyone see it different?
Seems your personal goals are limited by GPU time, so option 3 appears fastest- you can run CPU tasks and GPU tasks at the same time and finish in 85 days. But then, you could also add 10% to remaining P-1 bounds and maybe still find factors faster than TF, further reducing required GPU time.

2021-04-22, 02:52   #422
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

32×5×103 Posts

Quote:
 Originally Posted by VBCurtis Seems your personal goals are limited by GPU time, so option 3 appears fastest- you can run CPU tasks and GPU tasks at the same time and finish in 85 days. But then, you could also add 10% to remaining P-1 bounds and maybe still find factors faster than TF, further reducing required GPU time.
Makes sense.
At the present time there are more total contributions than CPU.
In that state it is better to NOT go to extreme P+/-1.
If GPU resources diminish then I will lean to MORE P+/-1.

2021-04-22, 04:16   #423
James Heinrich

"James Heinrich"
May 2004
ex-Northern Ontario

25·3·5·7 Posts

Quote:
 Originally Posted by kruoli Thanks for the page! Maybe you could add a NF/F column? I'm eager to see when the first new factor gets found with P+1.
There is now a factor column.

2021-04-22, 07:01   #424
ATH
Einyen

Dec 2003
Denmark

2×1,567 Posts

Quote:
 Originally Posted by James Heinrich Easily done. P+1 has never found a Mersenne factor, therefore optimal effort to spend on it is zero.
User "nordi" found the first factor: 287873 : 167460871862758047584571103871

30 digits and 97.1 bits, nice. From the timestamps it was the 92nd reported curve, but he reported 52 more in the same batch after the factor, so really it was the first factor in 144 curves from all up to and including 2021-04-22 06:48:xx.

Last fiddled with by ATH on 2021-04-22 at 07:15

 2021-04-22, 10:08 #425 axn     Jun 2003 136216 Posts Cunching the numbers on chalsall's GCE runs: Code: 6532 0.321 0.176913655848132 7685 0.364 0.170513988288874 8956 0.401 0.161188030370701 9502 0.437 0.165565144180173 That is Runtime(s), Prob(%), Prob/Hr. As you can see, with increased B1, there is a slight drop in Prob/Hr metric, but it is fairly flat. That means we could probably go with higher B1/B2 and still be similarly productive. However, it is still very low - 1 factor every 600 hours on a 4 core GCE machine One thing that puzzles me is the fairly low B2/B1 ratio. Given how much slower stage 1 is compared to P-1 stage 1, I would've expected it to be a lot higher. I would like to try out higher B2/B1 ratios (maybe 100x). Give me some time to get some probability estimates using the higher ratio. I have enough runtime data to accurately model Prob/Hr on that GCE machine -- I just need the probability figures.
2021-04-22, 11:46   #426
axn

Jun 2003

2×3×827 Posts

So after further crunching, I noticed that the GCE machines were producing inconsistent timings. After correcting for it, there was a much more pronounced loss of efficiency (prob/hr) as you go higher B1. So considering that, I think B1=600k is about as high as I would recommend.
The good news is that, I made a mistake in the previous assignment. I kept the TF depth as 75, when actual depth for 42.6 range should've been 74. That improves the probability a bit.

Keeping that in mind, here are the updated assignments. I am still leaving B2 selection up to P95. There was no improvement going to larger B2. I have removed the 5 that were completed.
The probability of success is about 1 factor in 500 hours of a 4 core GCE (give or take - there is natural variability in machine performance). It is up to you whether you consider this worthwhile.
Attached Files
 assignments.txt (10.7 KB, 10 views)

2021-04-22, 14:24   #427
masser

Jul 2003

110010010102 Posts

Quote:
 Originally Posted by VBCurtis Seems your personal goals are limited by GPU time, so option 3 appears fastest- you can run CPU tasks and GPU tasks at the same time and finish in 85 days. But then, you could also add 10% to remaining P-1 bounds and maybe still find factors faster than TF, further reducing required GPU time.
I second the recommendation to run CPU and GPU tasks simultaneously. Regarding the P+1, I see two arguments for it. First, in some domains, tasks that take 23 days to save 1 day are definitely valued. Second, P+1 is new for the project, so collecting some data at this stage could be very helpful to the project.

One more reminder about your estimates, although I'm sure you know this, each task is slightly parasitic to the other tasks in terms of lowering probabilities or number of factors found. For instance, TF will find factors that P+1 or P-1 might find. Of course, each method will be the quickest way to find a certain factor; too bad we don't know in advance.

Last fiddled with by masser on 2021-04-22 at 19:12

2021-04-22, 14:35   #428
chalsall
If I May

"Chris Halsall"
Sep 2002

2×4,787 Posts

Quote:
 Originally Posted by axn The probability of success is about 1 factor in 500 hours of a 4 core GCE (give or take - there is natural variability in machine performance). It is up to you whether you consider this worthwhile.
Thank you for your efforts. But for my ranges, I think doing deep P-1'ing is more cost-effective.

2021-04-22, 17:14   #429
axn

Jun 2003

2·3·827 Posts

Quote:
 Originally Posted by chalsall Thank you for your efforts. But for my ranges, I think doing deep P-1'ing is more cost-effective.
Understood.

 Similar Threads Thread Thread Starter Forum Replies Last Post jschwar313 GPU to 72 3 2016-01-31 00:50 Batalov Factoring 6 2011-12-27 22:40 jasong jasong 1 2008-11-11 09:43 devarajkandadai Math 4 2007-07-25 03:01 WraithX GMP-ECM 1 2006-03-19 22:16

All times are UTC. The time now is 12:10.

Thu May 13 12:10:19 UTC 2021 up 35 days, 6:51, 1 user, load averages: 1.83, 1.88, 1.92