mersenneforum.org > Data Thinking out loud about getting under 20M unfactored exponents
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2021-06-02, 17:21   #474
chalsall
If I May

"Chris Halsall"
Sep 2002

26E716 Posts

Quote:
 Originally Posted by LaurV Related to your wish that we move to P-1, we may try to pursue Chris to serve us P-1 assignments for our colab instances (and we will take care of the colab side). Maybe that's a good idea, we get rid of the headache with reserving the work, adding it to colab, and reporting the results (right now, manually).
Doable.

I've actually been using my fourteen (14#) (CPU only) Colab instances to clean up after those who complete an FTC without first doing a P-1. Sometimes preemptively; in 103M for example...

 2021-06-02, 20:13 #475 pinhodecarlos     "Carlos Pinho" Oct 2011 Milton Keynes, UK 3×1,657 Posts Happy to join with 10 Colab sessions but will need some guidance.
2021-06-02, 21:28   #476
chalsall
If I May

"Chris Halsall"
Sep 2002

26E716 Posts

Quote:
 Originally Posted by pinhodecarlos Happy to join with 10 Colab sessions but will need some guidance.
Copy. Thanks.

2021-06-03, 04:10   #477
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

19·251 Posts

Quote:
 Originally Posted by LaurV So, why to stop there? James' site allows x.xxM ranges for smaller exponents (and only xx.x for larger expos). So, following the idea, every x.xxM range (i.e. 10k) should have less than 200 unfactored expos.
I'd have to look back through this thread but someone asked the same question a few years ago.

The problem is that at this fine of a breakdown there are some serious outliers and so few exponents to work with.
Not even trying I found for example (there are worse):
26.70M 232 Unfactored (33 to get under 200).
Each bit level of TF will find about 2 factors with only 232 exponents.
So via TF only that is 16 more bit levels....with luck maybe only 14.
So that is TF 73-87.
That is almost 1,200,000 GhzDays per exponent; 8 months with my 2080Ti per exponent.

Assuming we agree that is beyond reasonable we need to find some factors via P-1.
Lets say we want to save 7 bits of TF so we need about 14 P-1 factors from these 232 exponents.
We need about a 6% increase in current P-1; so we will need to run P-1 with a 10.5% expected success rate to be safe.
That is 100GhzDays per exponent x 232 = 23,200 to get these 14 factors.
The better part of a year for a reasonable PC.

However there is another issue.
TF and P-1 can find the same factors so the more P-1 that is done the lower the chance of finding a TF factor and vice versa.
If we were to find these 14 P-1 factors then the TF success rate will drop; or in other words it will not save 7 levels of TF.

OKAY too much blabbering; you see where I'm going.

------------------------

That all said maybe once the sub-2000 project is complete the hardware will allow us to reconsider sub-200.

2021-06-03, 13:45   #478
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

9,787 Posts

Quote:
 Originally Posted by petrw1 The problem is that at this fine of a breakdown there are some serious outliers and so few exponents to work with.
Of course you are right, and the fact that it gets more and more difficult as you get deeper into the mud is plain clear. To get under 20M for all Gimps range is the easiest. Then, zoom in and find the outliers, magnitude by magnitude. I am still fighting with 1.71M for a while, but I am not going to do that forever, I also have a life
But I couldn't stop boasting about the P+1 success in 1.89M and about finding over 30 factors in 26M. Right now, they are more, as I moved to 27M and found 5 factors there today too.

 2021-06-09, 14:21 #479 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 9,787 Posts yarrr This almost passed unobseved: Code: 1717043 F-PP1 Start=2/7, B1=5000000, B2=365000000, Factor: 36120234091485938570203343 One more to go (for which, I am going to raise all 200 candidates one bitlevel, maybe get lucky - and stop if I get lucky). Last fiddled with by LaurV on 2021-06-09 at 14:24
 2021-06-10, 05:45 #480 axn     Jun 2003 19×271 Posts 3-4m is done The last two ranges 3.7 & 3.9 were done today, thus completing 3-4m. I had some TF help from anonymous benefactor which greatly accelerated 3.9 range. Once the pending P-1s from 3.7/3.9 ranges are completed (few days to couple of weeks), I'll move over to 4.1 range. I've been prepping that range with 68-70 TF.
 2021-06-12, 07:21 #481 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 9,787 Posts Is anybody doing P-1 in this range? I found about 15 factors in the last 4 days, but only 11 of them are reflected in the table, therefore the 12-th is from somebody else (I don't know which 12th). If that's a TF/P+1/ECM factor, no harm, but if that's a P-1, then we are duplicating the efforts. I started when 2076 candidates were left and (after a discussion with Wayne on PM) I calculated my B1 and B2 to have a 100% theoretic chance of finding 77 factors, considering an average of the TF and P-1 already done. Then, I "rounded up" them to "look nice", i.e. being prime, and containing a sequence of interesting primes too, as a substring that's how I ended with B1=23-29-31-9 (sorry, -31-3 was not prime), and B2=61-89-1103 (107x was not prime, and 1103 is a factor of M29!). For who's asking. These are nice, round numbers. Don't tell me that numerology is not catchy! Joking apart, with the default TF of the range the two limits would have a chance to get a factor in 10 trials, but considering that the range was over-factored, to 74 bits, the chance is just 1 factor in about 17 or 18 trials. However, the range had average P-1 done too, which "pulled out the low hanging fruits", so the real chance is somewhere at 1 in 23 to 1 in 26 (depending on the P-1 already done for each, I didn't calculate exact, only took an "eye average"). This would cover for the 77 factors (which, in 2076, means 1 in about 26.9, plus the luck ). Up to now, it fits, with 77 factors to find I should find about 7.7 in every 35.1x range, and I have 15 in the first 2 ranges, plus a bit. Last fiddled with by LaurV on 2021-06-12 at 07:56
 2021-06-12, 08:20 #482 axn     Jun 2003 19×271 Posts Code: 35130749 227470147005389851276513 2021-06-10 Sid & Andy F-PM1 B1=1500000, B2=45000000
2021-06-12, 08:38   #483
axn

Jun 2003

19×271 Posts

Quote:
 Originally Posted by LaurV However, the range had average P-1 done too, which "pulled out the low hanging fruits", so the real chance is somewhere at 1 in 23 to 1 in 26 (depending on the P-1 already done for each, I didn't calculate exact, only took an "eye average").
The real chance is more like 1 in 36, so you might find something like 60 factors. You could fall short by 15 factors in clearing this range with this P-1.

 2021-06-12, 12:26 #484 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 9,787 Posts Oh. Then I should either raise the limits, or save the checkpoint files to avoid work duplication in the future if me or somebody else will wish to extend the limits. BTW, can gpuOwl extend B1? (I remember getting errors like "wrong B1, using the one from saved checkpoint" or so).

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