Thinking out loud about getting under 20M unfactored exponents

[lycorn]

Just finished the 18M range to 70 bits.
248 factors found.
Starting 17M.

[petrw1]

Originally Posted by lycorn

Just finished the 18M range to 70 bits.
248 factors found.
Starting 17M.

[lycorn]

17M finished to 70 bits.
183 factors found.
16M to start in a few days.

[petrw1]

12 more ranges cleared: 2.8, 2.9, 30.0, 30.9, 31.3, 31.4, 31.8, 32.2, 33.4, 35.9, 37.4, 39.4

166 total ranges cleared or 33.40%
14 Ranges with less than 20 to go.

1,608 more factored (23,083 total)....41.80% total factored.

Continuing to get lots of great help. THANKS

Thanks again for everyone contributing.

[petrw1]

Briefly I am working on getting ALL "100K ranges" to under 2,000 unfactored exponents.
So, to be clear, I am finding factors; I am NOT looking for primes.

"100K ranges": Exponents from 3.0Million to 3.1M; 56.6M to 56.7M; 993.4M to 993.5M.

To date all ranges under 3.1M are "cleared" (under 2,000 unfactored).
Effort will NOT be required over 86.4M; these ranges will ultimately clear via the current prescribed TF levels and P-1.

I started this personal sub-project July of 2017 (almost 3 years ago).
I have been primarily focused on ranges up to 60M.
As of the start date there were 498 ranges to go (out of a possible 600).
As of today that count is at 332.

Finally, there are 11 ranges in my sideview mirror between 60.0M and 86.3M.

The required factors can be found via 1 of 3 methods:

1. Trial Factoring (TF): Can be used on any exponent but are most efficient on higher Exponents and at lower Bit Levels.
2. P-1: Can be used on any exponents but are most efficient on lower Exponents.
3. ECM: Best suited for the LOW Exponents (under about 10M).

========== HOW CAN YOU HELP? =======
First, keep in mind that most exponents in the ranges of interest have already had TF and P-1 to the prescribed levels required before PrimeNet will assign LL/DC/PRP tests.
In order to find the required factors more aggressive effort is required.

Most importantly, if the work to be done is NOT assigned with PrimeNet please let others know here where you plan to work.

1. Look here for ranges with more than 1999 unfactored: https://www.mersenne.ca/status/tf/0/0/4/2000
Use a Zoom Level of 0.1M.

2. Determine which range you want to work on and make note of:
- How many factors are required
- The current TF bit level
- How well P-1 has been done using: (Sort the results by lowest B2 and B1) https://www.mersenne.org/report_fact...xp_hi=20099999

3. Determine the best factoring method for the range chosen. Consider:
- For TF: GPUs are best for TF. A bit level of TF will find about 20 - 25 factors; but each successive bit level takes twice as long as the previous bit level.
- For P-1: P-1 requires LOT of RAM. The success rate is based on the difference between the P-1 already done and the P-1 you could do with higher B1/B2 values: This tool helps calculate the expected probabilities and effort required: https://www.mersenne.ca/prob.php
- For ECM: Again only for lower exponents.

4. Advertise here and then get/make the required assignments.
--- The effort required for your chosen work can be determined here:
https://www.mersenne.ca/credit.php

5. Have fun; good luck and Thank You.

========== The sample link provided tells me ============
The link I provided above for 20.0M to 20.9M shows that for 20.4M
- 2,048 are unfactored; 49 factors are required to get this count UNDER 2000.
- It is currently factored to 70 bits.

- These exponents are probably too high for ECM.

- If I choose TF to 71 I can expect to find about 20 more factors with an effort of about 23,900 GhzDays using the above tools. If your GPU does 1,000 per day that is 24 days of work.

- If I choose to then TF to 72 it will find about 20 more but this time taking 48 more days.

- I could consider some aggressive P-1. I can see that there are several hundred exponents that based on current B1/B2 had a 3% or less odds of finding a factor. If I use larger B1/B2 that give more an extra 2% or better chance of finding a factor (statistically: 1 in 50) for an effort of about 2.5 GhzDays each P-1. 125 GhzDays per factor on average. This is probably about a week per factor on a decent current PC.

What might I do/recommend.
- At least 1 more bit level of TF; 2 if you have an upper end GPU.
- Then some aggressive P-1 with my CPU.

P.S. My current focus is the remaining 21 ranges between 40.0 and 49.9M.
I am doing aggressive TF and P-1.

=========== THANKS FOR YOUR TIME =========

[VBCurtis]

If I were to dabble with ECM in the 4.0M block, should I test the numbers that have been advanced to 70 bits with the idea that TF has given up, or should I test the ones still at 69 with the idea that there are more small factors to be found?

I won't be doing very much work, just a core or 4 until I get bored of not finding factors.

[masser]

Originally Posted by VBCurtis

If I were to dabble with ECM in the 4.0M block, should I test the numbers that have been advanced to 70 bits with the idea that TF has given up, or should I test the ones still at 69 with the idea that there are more small factors to be found?

I won't be doing very much work, just a core or 4 until I get bored of not finding factors.

Could you run P-1 on that range instead? There are many candidates with B1 < 200,000 and B2 < 4M.

If you are set on running ECM, I would say focus on the candidates at the 68 bit TF level.

That range is close enough to 1999 unfactored, that you might be able to reach the target with either factoring method.

[petrw1]

Originally Posted by masser

Could you run P-1 on that range instead? There are many candidates with B1 < 200,000 and B2 < 4M.

If you are set on running ECM, I would say focus on the candidates at the 68 bit TF level.

That range is close enough to 1999 unfactored, that you might be able to reach the target with either factoring method.

I tend to agree.
I hope I am not speaking out of turn but I seem to recall a post or two from Bob Silverman … who knows WAYYYYYY more about any of this than I do … that even for these small exponents P-1 is more efficient that ECM.
As well in these low ranges you do NOT need a lot of RAM to run decent P-1.

For example: https://www.mersenne.ca/prob.php?exp...ts=68&K=1&C=-1
6% chance of finding a factor for only 0.6 GhzDays and with only a few hundred Meg of RAM.

Thanks; welcome and good luck.

[petrw1]

There are a couple dozen ranges, most that have had aggressive P-1 done on the bulk of the assignments in the range as well as deep TF....
And still they stubbornly refuse to give up easily.

These ranges will need either or both of:
1. Even more aggressive P-1 on those exponents will current mediocre P-1. For this you will want a (or many) powerful CPU with lots of RAM
2. Deeper TF; where each TF assignment will take 100 or more GhzDays. For this you will want a (or many) powerful GPU.

--- And you'll need some patience.

I'll give some examples; I'll give range; current TF level; remaining Factors required:
These 3 ranges could benefit from extra P-1 on small subset of the exponents.
34.4; 74 bits TF; 60 Factors
35.1; 74; 77
35.3; 74; 64

These 4 ranges are NOT yet aggressively P-1'd.
42.6; 74; 88
43.0; 74; 84
48.4; 74; 83
49.6; 74; 81

These ranges have had aggressive P-1.
56.8; 74; 39
58.7; 74; 37
59.4; 74; 46
68.4; 75; 30
73.1; 75; 36
73.5; 75; 43

Thanks and good luck.

[VBCurtis]

I'm fairly certain RDS pointed out the futility of running P-1 on numbers that had already been P-1'ed; recommending ECM instead. I went looking for his posts, but didn't find anything.
I don't have a GPU setup, and with P-1 now on GPU it feels like the best use of this old laptop (Broadwell ultrabook, 2-core) is to dabble in P95-ECM. I'll run curves for a week or so, perhaps until a factor turns up, and then I'll do the same with P-1.

Does that 6% chance of factor take into account the previous P-1 run that was done? The site doesn't appear to indicate it does, in which case it's a pretty big exaggeration of the actual chance of factor. Meanwhile, ECM doesn't care what prior P-1 has been done.

I'll gather some data and see if there's a clear winner- if there isn't, I'll do ECM just for something different.

[petrw1]

Originally Posted by VBCurtis

I'm fairly certain RDS pointed out the futility of running P-1 on numbers that had already been P-1'ed; recommending ECM instead. I went looking for his posts, but didn't find anything.

You could very well be correct. I think what I was recalling is that when neither has already been done then P-1 is more effective than ECM....though I'm not sure at what low levels of P-1 that MORE higher P-1 is better than ECM.

Does that 6% chance of factor take into account the previous P-1 run that was done? The site doesn't appear to indicate it does, in which case it's a pretty big exaggeration of the actual chance of factor. Meanwhile, ECM doesn't care what prior P-1 has been done.

No, sorry it does not. I mean to then forgot.
The current P-1 ranges from about 2.4% to 8.2% (yes, someone went real hard on some … also factored them to 70 bits).
But about 40% of the exponents are under 3.42%.
So, yet for these the net difference (vs 6%) would be about 2.5 - 3.5%.
And 8.15% is only 2 GhzDays