Let's Optimize P-1 for low exponents. TL;DR in post #1. More in posts 60 and 61.

[petrw1]

834 more P-1 required exponents factored (some may have been TF or ECM)
9,321 more exponents with P-1 completed

New ranges cleared: 0.2, 4.1, 4.3, 12.1

On the LOW TF wave front:
All exponents above 23.8M at 73 bits (TBH just a few stragglers at 25.0)
All exponents above 11.8M at 72 bits.

Woot Woot!!!

I also updated assignment ranges based on activity in the last month...correct me if I missed any

[Denial140]

P-1 on 4.96M should finish up over the next few days. It probably won't quite meet the goal of below 200 unfactored, with 6 factors found by TF and 11 by P-1 so far. As of now it's sitting at 202 unfactored, which will hopefully be cleared up by a little bit of ECM (thanks to Cong Shengzhuo for the ECM work he has done so far on this range, which has found 1 factor unless I missed any)

In terms of P-1, I'll be looking at 2.41M and 3.94M next with the same goal :)

[kruoli]

Originally Posted by kruoli

Next, I would like to reserve 100K-150K.

This is still being worked on actively. I know that there have not been any reported results in a while, but I can assure you that I have a machine crunching through stage 1 of all exponents. As soon as I have a high-memory machine with spare cycles, I will resume stage-2'ing them.

[congsz]

My situation is similar. I currently have 2 machines available. One is working on 4.96M ECM, with results being submitted. The other is working on 8.92M P-1 Stage 1 (with high bounds), with no results being submitted at the time.
So there will be a period of time when I am not submitting any P-1 results. But I am still actively working in the range, so I will keep my reservation.

@Daniel (Denial140): I have found 1 ECM factor so far in 4.96M range. You didn't miss any.

P.S.:
I am dreaming of factoring 6.48M VERY DEEPLY if I can have one (or more) new, fast & high-RAM computer in a few years' time, in order to let the number of unfactored exponents drop to below 200.
The current number is 241. So, this dream is highly unrealistic (or almost impossible), It is highly likely that this dream will not become a reality before 2040, unless new changes as big as the implementation of v30.8 P-1 occur.
Can anyone help calculate if it is likely to reach <200 unfactored, with P-1'ing B1=1e9 and >=200GB RAM (really demanding), ECM-ing every exponent to T40 (far more demanding, requires cooperation from users), along with adequate P+1?

[petrw1]

Originally Posted by congsz

I am dreaming of factoring 6.48M VERY DEEPLY if I can have one (or more) new, fast & high-RAM computer in a few years' time, in order to let the number of unfactored exponents drop to below 200.
The current number is 241. So, this dream is highly unrealistic (or almost impossible), It is highly likely that this dream will not become a reality before 2040, unless new changes as big as the implementation of v30.8 P-1 occur.
Can anyone help calculate if it is likely to reach <200 unfactored, with P-1'ing B1=1e9 and >=200GB RAM (really demanding), ECM-ing every exponent to T40 (far more demanding, requires cooperation from users), along with adequate P+1?

For P-1 you yourself can use this
1. Enter the current bounds to show the current average success rate.
2. Enter your proposed bounds to show the expected success rate.
3. Calculate the difference and thereby the expected new factors.

I did this and got:
1. Some were at 3.8%; some at 5.5%
2. Using 1e9 and 1e13 for bounds (I guessed at the B2 but with 200G it's probably reasonable) I get 25.5%
3. Difference is about 20%. With 241 exponents you can expect 20% of 241=48 factors.

That suggests you chance of succeeding are pretty good.
These exponents have not had much ECM yet so this makes the P-1 success rate more accurate.

So ECM may not be necessary.

I don't understand ECM success rates as well but I was told a while back that you can use this:
1. Determine how many bits of TF correspond to T40 (40 digit factors)....132 bits I believe.
2. The ECM success rate will be similar to doing TF to that many bits (in much, much less time).
3. You need to start your calculation at the current bit level (72).

What I can't intelligently discuss is how much overlap of factors there will be between the ECM and P-1.
But you definitely cannot just add the two expected factor counts.

Alternatively you could find a middle ground with a little less P-1 and some reasonable ECM to find the same number of factors with likely less time spent.

[Denial140]

Originally Posted by congsz

P.S.: I am dreaming of factoring 6.48M VERY DEEPLY if I can have one (or more) new, fast & high-RAM computer in a few years' time, in order to let the number of unfactored exponents drop to below 200.
The current number is 241. So, this dream is highly unrealistic (or almost impossible), It is highly likely that this dream will not become a reality before 2040, unless new changes as big as the implementation of v30.8 P-1 occur.
Can anyone help calculate if it is likely to reach <200 unfactored, with P-1'ing B1=1e9 and >=200GB RAM (really demanding), ECM-ing every exponent to T40 (far more demanding, requires cooperation from users), along with adequate P+1?

I think this would be more than sufficient. I did a test on a couple of exponents a while back and with 32GB RAM it had B2~=2500xB1. For 200GB this should translate to B2 > 1.5e13, so expected >= 48 factors as Wayne calculated. I'm not really familiar with how ECM and P-1 probabilities affect eachother, but ignoring P-1, I think you would expect around 20 factors from a full T25. Of course, at this size of exponent, even this is a significant effort. But it's not so out of reach as it may seem.

That being said, I for one am leave this range for you to enjoy at a later date, although I would be happy to help if you wanted.

[Andrew Usher]

The B2/B1 ratio it gives you will not be constant, but decrease with increasing B1 and exponent (ratio of FFT size to memory). So that may be a bit optimistic, but still B1=1e9 is massive there.

That ECM approximation is good if you get it to a T-level significantly higher than TF; if not (as is common here), it;s higher per curve but I'm not sure of a good way to approximate it and I wish there were a calculator for it. To determine the overlap between the two, one would only need the distribution of (possible) P-1 factors by size, which is certainly possible and, I believe, actually behind P-1 calculators.

[Denial140]

Originally Posted by Andrew Usher

The B2/B1 ratio it gives you will not be constant, but decrease with increasing B1 and exponent (ratio of FFT size to memory). So that may be a bit optimistic, but still B1=1e9 is massive there.

The tests I was talking about were on the same range of exponents, and my general experience has been that B2/B1 ratio increases with B1. See M4962187 vs M4962193, for example. It's certainly possible that this breaks down at higher B1, so I'd be happy to see data supporting that if you have any.

[chris2be8]

Would P+1 be useful to help get 4.96M or 6.48M below 200 unfactored exponents?

[petrw1]

Originally Posted by chris2be8

Would P+1 be useful to help get 4.96M or 6.48M below 200 unfactored exponents?

Moreso for 4.96; it would seem 6.48 will complete with P-1 and/or ECM; both more efficient than P+1

[Andrew Usher]

Originally Posted by Denial140

The tests I was talking about were on the same range of exponents, and my general experience has been that B2/B1 ratio increases with B1. See M4962187 vs M4962193, for example. It's certainly possible that this breaks down at higher B1, so I'd be happy to see data supporting that if you have any.

You're right and I got confused (thinking about runtime instead). The B2/B1 ratio should increase with B1, just not as fast as with unlimited memory (when B2 ~ B1^2 ideally with the new algorithm).