Thinking out loud about getting under 20M unfactored exponents

[lycorn]

Originally Posted by Gordon

Come down to the *low* side - under 5k...

That´s too low for the GPU TF programs we have available. Or did you want to mean 5M?

[VictordeHolland]

Originally Posted by Gordon

Come down to the *low* side - under 5k...

Exponents <5000 all have had at least a t40 of ECM done, most of them even t50 or more. Please don't use TF in that region, it's a complete waste of time/resources.

[LaurV]

Originally Posted by lycorn

That´s too low for the GPU TF programs we have available. Or did you want to mean 5M?

Originally Posted by VictordeHolland

Please don't use TF in that region, it's a complete waste of time/resources.

There are modified versions of mfaktc that allow factoring "over 2k", but we agree with Victor that TF there is a totally waste of time and resources. They had tons of ECM and P-1 done, so the chance a factor under 100 bits escaped is smaller than any epsilon...

[Gordon]

Originally Posted by VictordeHolland

Exponents <5000 all have had at least a t40 of ECM done, most of them even t50 or more. Please don't use TF in that region, it's a complete waste of time/resources.

Sorry, I didn't make that clear, it's ECM that I'm doing...

[snme2pm1]

Originally Posted by petrw1

(REMINDER: My lofty goal is to get all 0.1Million ranges under 60Million to under 2,000 unfactored. With the deeper factoring for ranges over 60Million I expect virtually all these ranges to be cleared in this way).

What was the basis for reliance on the notion of unfactored <2000 per 100k goal for below 60M or any other range for that matter?
Perhaps there is a graph somewhere that supports the accompanying notion that the goal posts might be shifted for different, particularly higher, exponent million zones?

By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here!

[Uncwilly]

Originally Posted by snme2pm1

By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here!

Enough that during the winter in central Canada he must needs keep a window open in a room where the beasts reside.
https://mersenneforum.org/showthread.php?p=502902

[petrw1]

Originally Posted by snme2pm1

What was the basis for reliance on the notion of unfactored <2000 per 100k goal for below 60M or any other range for that matter?
Perhaps there is a graph somewhere that supports the accompanying notion that the goal posts might be shifted for different, particularly higher, exponent million zones?

By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here!

GIMPS as a whole has well defined standards of how deep to factor all ranges; though GPUs have increased these somewhat. I am not trying to undermine that in any way. I see my interest as more custodial; cleaning up behind them.

Some time back someone, on the topic of milestones, noted that having less than 20,000,000 unfactored exponents would be monumental though admittedly a LONG way off.
See unfactored total at the bottom of this (just over 21.3 Million): https://www.mersenne.ca/status/tf/0/0/1/0

That got me to thinking as I noted in the first post of this Thread:

Thinking out loud about getting under 20M unfactored exponents
Breaking it down I'm thinking if each 100M range has less than 2M unfactored we have the desired end result.
Similarly if each 10M range has less than 200K unfactored...
or each 1M range has less than 20K unfactored...
or each 100K range has less than 2,000 unfactored.

So I decided to make it a sub-project of focus for me.
Happily several others found it interesting as well and have been helping out.
A huge thanks to Chris for volunteering to let GPUto72 spider the TF work assignments.

When I drilled down into the same link above I noticed that ranges 60M and above would mostly end up with less than 2,000 on their own due to the deep factoring going on at GPUto72.
There are a few exceptions but not many. Some day I may look there too.
So my main focus and tracking has been under 60M though I do occasionally "spy" on the larger ranges.

Still I wanted to work on this project in a way that would benefit GIMPS as a whole if I could.
I noted that the current DC wave-front is in the 40M area so I realized that factoring there would reduce the DC workload at the same time.
Hence my main focus that last couple years has been in the 40M and 50M ranges.

My 3-pronged approach has been to find ranges with 2000+ unfactored. Then:
1. Find exponents with poor P1 bounds (mainly with B1=B2) and redo them with CPUs. I am going beyond the default bounds set by Prime95. Mostly B1=1000000; B2=20000000 in the 50M ranges. This has cleared several ranges; as in <2000.
2. Use the GPUs to factor remaining ranges deeper. This cleared many more.
3. For CPUs with slower processors or less RAM run P1 or ECM in the very low ranges; i.e. under 5M. I have cleared about half a dozen ranges there. Granted normal ECM work would probably have done so itself over the next few years.

I would recommend the same approach for anyone interesting in helping out. We only ask that there is some communication to ensure no toe-stepping.

In the 50M range I started with 40 ranges (out of 100) with 2000+ unfactored. I am a few weeks away from getting that count down to 9 and factoring over 600 exponents; thereby eliminating a DC for these.

Most of my effort has now shifted to the 40M ranges. It had over 60 ranges to go when I started this sub-project. It is now under 50 ranges to go and dropping.

Others are working in lower ranges; mostly 30M with great progress.

I started tracking about 16 months ago. At that time for the ranges under 60M there were almost 500 ranges over 2000 unfactored (out of 600 total). We are now closing in on 400.

Thanks again to all contributors and to those showing an interest.

[petrw1]

Originally Posted by snme2pm1

By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here!

I took a risk and bought one of the newly announced RTX 2080Ti GPUs in the fall. The first was faulty and had to be replaced.
I also bought an 8-core i7-7820x CPU and put in it 32GB of DDR4-3600 RAM.
These were my personal reward for taking one more contract at work when I would rather have been retired.

In total I have 2 GPUs:
GTX-980 at about 560 GhzDays/Day of TF
RTX-2080Ti at about 4,000 GhzDays/Day of TF

And the following CPUs. Only the 3570K (5 years ago) and the 7820X (this year) were bought new.
Collectively they complete over 200GhzDays/Day (45 assignments) of P1.
All 4 core except the 3 noted differently.
All but 2 are in my house....I think the only people with higher power bills have a grow-op in the basement.

Intel Core i5-2520M @ 2.50GHz (2-Core Laptop)
Intel Core i5-4310U @ 2.00GHz (2-Core Laptop)
Intel Core i5-2500 @ 3.30GHz
Intel Core i5-3570 @ 3.40GHz
Intel Core i5-3570 @ 3.40GHz
Intel Core i5-3570K @ 3.40GHz
Intel Core i7-6700 @ 3.40GHz
Intel Core i7-7820X @ 3.60GHz (8-core)

[snme2pm1]

Originally Posted by petrw1

When I drilled down into the same link above I noticed that ranges 60M and above would mostly end up with less than 2,000 on their own due to the deep factoring going on at GPUto72.

Don't let folk misunderstand, Wayne and I are friends that have collaborated previously.

I am yet to find an estimate analysis of probability for the composite of tests out to James's yellow marker, or some other criteria, that would leave unfactored candidates within a 100k exponent region at something near 2000.
It seems to be somehow close to a likely outcome for some regions, but I suspect, as Wayne seems to acknowledge, that different regions might have different probability of survival of a candidate, again based on some criteria.

I feel somewhat awkward about reliance on such an arbitrary number, and that perhaps there might be a corresponding interpretation of an exercise to chase down exponents within localized 100k regions that didn't achieve the expected probability of finding a factor.
I suspect that the arithmetic has been done before this time, so is there a suitable link that can be cited?

[ATH]

The fastest way to get under 20M unfactored exponents, if you skip your 2nd goal of 2,000 unfactored every 100k, is probably to use GPU to trial factor the range 100M-1000M. There are probably enough factors hidden there without doing very deep factoring.
But this way you contribute more immediately to DC instead of contributing to future LL and DC.


Right now there are 29,544,903 of 50,847,534 exponents with at least 1 factor, so 30,847,534-29,544,903 = 1,302,631 left until 20M unfactored.

Last 365 days that number of factored exponents went up with +267,160, so if that speed is kept it will take just under 5 years:

http://hoegge.dk/mersenne/GIMPSstats.html

[lycorn]

Over the last 3 or 4 months we have had a very large contributor (sometimes over 1500 factors in a day), but it's apparently cooling down :(
Let's see how it goes.