COMPLETE!!!! Thinking out loud about getting under 20M unfactored exponents

[petrw1]

Originally Posted by lycorn

Looking at the current twok table I noticed the largest stumbling block we have on our way is the 12M range. I would like to work there for a while, so here´s my query:

What would be the most productive/sensible approach?

i) TFing to 73: that would cost ~7.6 GHz-day per trial, for a reasonable expectation of 1 factor per 100 trials. That amounts to circa 760 GHz-days per factor found. Not free...

ii) Extending the current bounds for P-1: many exponents have been tried to relatively low values of B1, B2; there is a significant number with B1 <= 150,000 and B2 less that 20xB1. That might be an interesting opportunity. Using bounds 50x larger than the smallest ones currently tried, the probality of finding a factor is ~ 5.5%, for a cost of 9Ghz-day per trial. That would be less than 180 GHz-days per factor found. It sounds a lot more appealing than TF.

iii) ECM doesn´t appear to be competitive for exponents this large. Running 280 curves @ B1 =50k, B2=5e6 would cost ~ 164 GHz-days for a relatively low probability of finding a factor, giving the P-1 and TF already done.

iv) P+1 might be an option, but I am not sure about what to expect. It seems to me that one should further explore the P-1 option (read: try higher bounds) before going down this route.

Thoughts? Suggestions?
Thanks in advance.

Note: I have permanent access to a GTX1660Ti for TF, and a i5-7400 (Kaby Lake) with 16 GB of memory. I also run several (free) Colab instances.

First off, thanks for taking up the challenge.

Analyzing the sub-ranges about half that will take some effort.... those over 70 is my opinion.

Range	To Go
12.0M	40
12.1M	88
12.2M	68
12.3M	118
12.4M	42
12.5M	30
12.6M	93
12.7M	88
12.8M	49
12.9M	74

To your points above:
i) TF to 73. Chris has this range (and all the rest) curated for TF73. Anonymous and others are working on these but could be 6 months from getting down to 12M.
Also, since these have had some, but not a lot of P-1, you should average closer to 1 factor per 80 attempts or about 25 per range.

ii) P1 is your best option for ranges this low. With lower exponents P1 is cheaper and TF more expensive.

iii) ECM is NOT as efficient as P1 for finding factors.

iv) P+1 is worse yet; it would be your last resort.

------- My humble opinion -------
This might be way more than you need or it might totally confuse you.
Feel free to reply accordingly.

Let your GPU chew on the worst ranges; ie starting on 12.3M.

Give your CPU the P-1; start with the easy ranges. But for each range set the bounds as required to get the required factors.
If you trust that Anonymous or you or someone else will eventually TF to 73 you can reduce these numbers by 25.
So for example: 12.0M only needs 40 factors ... it could be as low as 15 if TF73 gets there but assuming you choose to NOT wait:
40 is less than 2% of 2,039 exponents so you need your P1 to average 2% above what has already been done.
You could use 2.5% to be sure or stick to 2% and let TF clean up any you're short. I'll use 2% in my example and leave it up to your final say.

Looking here shows the current P1 done.
Eyeballing shows there are lots at, for example 150,000/3,075,000.
This shows you these had a 2.3% success rate. You need to average 2% more or 4.3%.
This shows you the required bounds and GhzDays to get 4.3%. Not bad, less than 1 GhzDay per test!

Similarly, if you consider the exponents currently at 200,000/4,000,000 you need new bounds of about 818,651/24,559,530 to get 4.58% at 1.18GhzDays per.

So what bounds should you use? I'd be lazy and guesstimate the overall average of the current P1 and add 2% (or 2.5%) to that number and use the resultant bounds for all my attempts.

So, 12.0 (and 12.4, 12.5 and 12.8) won't be bad.

At the other extreme lets take 12.6M at 93 ToGo (I'm assuming 12.3M is getting TF73 first).
This one needs 93/2,092 or a 4.45% P1 increase. This will be more challenging.
For example there are a lot currently at 300,000/6,000,000 for a 3.01% success rate.
7.46% (4.45% more) would need bounds of 4,728,944/165,513,040 at 7.53 GhzDays per.
Hmmm... I might consider more TF here first.

How about 12.2M with 68 factors? 68/2,067 = 3.29% increase.
This range has almost half currently at bounds 150,000/3,187,500 and lower. 2.32%
2.32% + 3.29% = 5.61%. Bounds required: 1,653,215/49,596,450 and 2.38 GhzDays. Not bad.
Or looking at 300,000/6,000,000 current at 3.02% + 3.29% = 6.31%: 2,344,628/82,061,980 at 3.73 GhzDays.
Not bad.

Now that I've written all this I think it's probably way more than you needed; you seem to understand the math/process. Sorry, but maybe this will help others.

Wayne

[lycorn]

@petrw1:
Thanks for taking the time to reply in such a comprehensive manner. Although, as you hinted, I understand the basics of the math/process, it´s always good to hear from someone deeply involved in this sub project and way more acquainted to its ins and outs than I.

I will probably start next week, and am considering to proceed along the lines drawn up in your post. The detailed choice of ranges/assignment of resources will then be posted here.

[petrw1]

...

[lycorn]

@chalsall,

I just started some tests on P-1 for the 12.00 - 12.05 M range. Could you please remove it from the available ranges?
Several results will be sent today, I hope.
Thank you.

[petrw1]

Originally Posted by 9vLYvxWUJ7Dy2Hb

Given that I'm only making minimal progress on this range and someone else (Sid & Andy) is having way more throughput I'll limit myself to everything below 31219961


This means the following range is up for grabs again: 31220003 to 31249993

31.2M is now complete.
Feel free to work on another range.
See here for available ranges:

The first post of this thread shows ranges above 20M claimed by workers.

Thanks

[petrw1]

And the last factor I found to complete the last range was over 116 bits ... and it was a Stage 1 factor.
35311457 F-PM1 2021-11-20 02:07 Factor: 113625742725813091246505895093165113 / (P-1, B1=2000000)
k is: 2^2 × 523 × 769 × 2399 × 425839 × 695411 × 1407751

If anyone has any assignments in the 3x.xM ranges you can release them for the sake of this project or let them finish ... it's your rig.

I expect Anton to finish 49.6M in the next week or so.

And with all the current help I expect all of 2x.xM to finish late summer 2022.

Thanks for all the help.
We're almost there.

Wayne

[petrw1]

masser reported in the last factor required for 14.0 just 1 minute earlier than my last factor for 35.3M.

For those who don't have the history 14.0 was the WORST range when this project started.
It required 297 factors.
He started working on it about April of 2020.
That's 20 months ... now that's patience and commitment.

Thanks

P.S. I sure hope I didn't steal your thunder by announcing this for you.

[masser]

As Wayne mentioned above, 14.0M is complete!

First off, much gratitude to Wayne, Chalsall and all of the GPU72 volunteers for helping with the final TF push. That effort shaved 2-4 months off of the 14.0M challenge. Recognition also goes to VBCurtis, for helping over the past year with ECM curves and some large-bounds P-1. His factors were particularly welcome as they seemed to arrive when my machines were in a factor drought. The recent upgrades to the factoring algos in Prime95 also helped tremendously, so thanks, as always, to George.

One of the main reasons for tackling the most difficult range in this sub-project was that, when finished, we might have a better sense of the effort required to clear the remaining ranges. So, here is some data. Upon completion (1999 unfactored exponents remaining) of the 14.0M range, the average P-1 bounds on the remaining candidates are: B1 = 7.6M, B2 = 340M. This corresponds to about 16.5 Ghz-days of P-1 on each candidate. The average number of ECM t25 curves completed on these candidates was 31; the P+1 effort is included in these counts, as well. In a very crude estimate, this corresponds to one P+1 test with B1 = 1.55M. The average TF bit-level achieved was 73.035.

The Under 2K subproject is GPU-heavy and my effort on the 14.0M range was CPU-centric, so the data above might not be directly relevant. Most of the remaining, difficult ranges will be TF'ed beyond 73 bits. That said, I think we now have a decent upper bound for the P-1 bounds on the more difficult ranges. For instance, 17.0M (156 factors to go) could probably be completed with TF to 74 bits and (P-1) B1 = 8M.

Thanks again, Wayne, for the fun challenge! On to 8.6M...

[axn]

Wow! Respect!

[chalsall]

Originally Posted by masser

One of the main reasons for tackling the most difficult range in this sub-project was that, when finished, we might have a better sense of the effort required to clear the remaining ranges. So, here is some data. Upon completion (1999 unfactored exponents remaining) of the 14.0M range, the average P-1 bounds on the remaining candidates are: B1 = 7.6M, B2 = 340M. This corresponds to about 16.5 Ghz-days of P-1 on each candidate.

Wow! SERIOUS respect!

It might be amusing to create a new metric for this project. Toy Stories...

"Oh, yeah... 14.0M took 3.7 Toy Story Movie (TSM) equivalents in compute..." (Pulling a number out of my butt... I have no idea how much compute went into rendering that movie... But it might be a cute thing to estimate; a bit of a nod towards Wayne's naming convention for his machines... )

masser, please let us know if you'd like 8.6M taken up to 73 in parallel. The Colab TF'ers can actually be given work sorted by B1 or B2 in (effectively) real-time.

[masser]

Originally Posted by chalsall

masser, please let us know if you'd like 8.6M taken up to 73 in parallel. The Colab TF'ers can actually be given work sorted by B1 or B2 in (effectively) real-time.

Thanks for the offer, but VBCurtis and I have it covered, I think. It will give our modest GPUs something to work on while we hammer on the range with P-1. Sorting by B1 or B2 will be a good feature as we approach the more difficult ranges.