20170726, 04:45  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2^{2}·1,163 Posts 
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 P1 could find factors much quicker. In either case it looks like this will be a very far off milestone. 
20170726, 07:48  #2 
Oct 2015
2×7×19 Posts 
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. Last fiddled with by 0PolarBearsHere on 20170726 at 07:49 
20170726, 10:43  #3 
"Victor de Hollander"
Aug 2011
the Netherlands
10010011000_{2} Posts 
And what would this accomplisch?

20170726, 16:03  #4 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2^{2}×1,163 Posts 

20170726, 19:48  #5 
Sep 2006
Brussels, Belgium
3213_{8} Posts 
If your best tool is a factoring machine you view everything as as entities to be factored. :)
Jacob 
20170726, 20:03  #6  
If I May
"Chris Halsall"
Sep 2002
Barbados
17×569 Posts 
Quote:
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 20170726 at 20:07 

20170726, 20:35  #7 
Aug 2006
3·1,993 Posts 
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 nonsqrtsmooth part (which dominates computationally) of Feitsma's algorithm for listing 2pseudoprimes. 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. 
20170726, 23:01  #8 
Nov 2008
3×167 Posts 

20170726, 23:25  #9 
"Forget I exist"
Jul 2009
Dumbassville
10000011000000_{2} Posts 

20170726, 23:52  #10 
If I May
"Chris Halsall"
Sep 2002
Barbados
17×569 Posts 

20170727, 04:40  #11 
Random Account
Aug 2009
79C_{16} Posts 
I believe just about everyone here recognizes the image I have attached. This ends at 2^{80}. 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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