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Old 2017-07-26, 04:45   #1
petrw1
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Default Thinking out loud about getting under 20M unfactored exponents

http://www.mersenne.ca/status/tf/0/0/1/0

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 did some Excel ciphering looking at:
- how many more factors are required in each range
- how many exponents need to be TF'd at the current bit level to get there (could require several bit levels to complete)
- how many GhzDays each assignment would take.
- I stopped at the 59M range thinking current GPU TF bit levels will factor adequately (most of the time) to get below my limits of interest here.

I did this for the 10M, 1M and 100K ranges.

Then I added it all up and came up with very roughly 250M GhzDays of TF with some ranges requiring up to 10 more bit levels of TF. WOW.

In perspective, my 1,000 per day GPUs would take 250K days: 685 years.

Oh dear; that's way more than I had expected.

Note: I only considered TF.
I understand that in some (many?) cases ECM (on lower exponents) and P-1 could find factors much quicker.

In either case it looks like this will be a very far off milestone.

Code:
=== Process where current B1=B2 first; then lowest current B1&B2.
=== Even when B2>B1 the current bounds are mostly quite low and factors are plentiful.
=== Judger is still systematically TF'ing to 75 bits where 20+ to go.   
=== I'd suggest not doing P1 on any ranges lower than TF75 beyond the first section below.

Range	ToGo	B1=B2	TFBits	Owns

=== Any in this group will clear with relatively low P1 bounds.
=== Something like 1M/30M should be more than enough.
29.7	2	761	75.000	Chris
28.5	6	323	75.000	Chris
24.0	6	250	74.000	Luminescence
24.8	8	517	74.337	Judger
25.7	11	739	75.000	
25.9	11	799	75.000	
29.0	14	718	75.000	
27.8	15	818	75.000	
24.9	16	757	74.445	Judger
24.2	17	616	74.302	
25.4	17	727	74.650	Judger
28.1	17	679	74.000	Kruoli
26.2	23	792	75.000	
23.9	25	633	74.000	
26.9	25	793	75.000	
23.4	27	12	74.000	
24.4	28	577	74.393	
28.0	28	538	75.000	
24.1	29	643	74.000	
22.4	31	0	74.000	
26.8	31	848	75.000	

=== Starting about here consider about 1.5M/45M though 1M/30M might do it.
26.4	43	812	75.000	
21.8	46	718	74.000	
21.7	49	819	74.000	
24.7	51	700	74.470	Judger

=== There are getting a little more dicey.
=== I'd be tempted to wait for Judger to TF75
=== But if you are ambitious consider 2M/60M as minimal bounds; even more near the end of this list.
27.2	61	835	75.000	
26.5	62	800	75.000	
21.9	72	333	74.002	
27.0	72	848	75.000	
25.3	77	766	75.000	
22.3	79	0	74.000	
29.8	91	796	75.000

Last fiddled with by petrw1 on 2021-10-19 at 03:19 Reason: Keeping the "Help Wanted" updates here on post 1
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Old 2017-07-26, 07:48   #2
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It just means we need more GPUs.
For instance if we can get 1000 high end GPUs on it, we could get it done in under a year based on your maths. We just need to find an organisation with a spare 800K USD who had a sudden urge to generously donate GPUs to anyone that requests one.

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Old 2017-07-26, 10:43   #3
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And what would this accomplisch?
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Old 2017-07-26, 16:03   #4
petrw1
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Quote:
Originally Posted by VictordeHolland View Post
And what would this accomplisch?
Absolutely nothing of consequence.
Nothing more than another milestone of interest to some.
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Old 2017-07-26, 19:48   #5
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If your best tool is a factoring machine you view everything as as entities to be factored. :-)

Jacob
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Old 2017-07-26, 20:03   #6
chalsall
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Quote:
Originally Posted by S485122 View Post
If your best tool is a factoring machine you view everything as as entities to be factored. :-)
Just to reflect Jacob... Sometimes it is worth the effort to think about what other people are thinking about...

In addition to the Philips, are you familiar with the Roberson? The hex?

I have actually watched people slam screws into wood using a hammer, because the Philips screws' heads were stripped with a screw driver which was too small.

I actually learned some new words (containing many symbols, including (!*%$@***!!!)) from men who should have understood the simplicity of the situation.

For what that is worth....

Last fiddled with by chalsall on 2017-07-26 at 20:07
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Old 2017-07-26, 20:35   #7
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Quote:
Originally Posted by VictordeHolland View Post
And what would this accomplisch?
I'm not sure what the OP has in mind, but I know that full factorizations of small Mersenne numbers are very useful. For example, they greatly speed up the non-sqrt-smooth part (which dominates computationally) of Feitsma's algorithm for listing 2-pseudoprimes. I've heard interest in extending his work beyond 2^64 so this isn't just academic.

As for finding individual factors, I don't know... I guess it just gives simpler/shorter certificates of compositeness.
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Old 2017-07-26, 23:01   #8
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Quote:
Originally Posted by VictordeHolland View Post
And what would this accomplisch?
because they are there and because we can :-)
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Old 2017-07-26, 23:25   #9
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Quote:
Originally Posted by VictordeHolland View Post
And what would this accomplisch?
if done high enough, in theory, it could deplete the candidate factors for larger mersenne numbers a bit.
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Old 2017-07-26, 23:52   #10
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Quote:
Originally Posted by science_man_88 View Post
if done high enough, in theory, it could deplete the candidate factors for larger mersenne numbers a bit.
Yeah... In theory....
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Old 2017-07-27, 04:40   #11
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I believe just about everyone here recognizes the image I have attached. This ends at 280. I suppose some here could comfortably TF to this level in a reasonable period of time. Of course, I do not know what most would consider "reasonable."

The last I heard, a computer "generation" was in the area of 18 months. It is probably less now. It would take many generations of tech growth to get to the level the OP was writing about.

Point: Let us do now what needs to be done now, and not think about the future.

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