20201105, 05:45  #1 
Feb 2019
China
59 Posts 
how to get F118 factor 1527888802614951*2^120+1?
1527888802614951*2^120 + 1
1527888802614951 has 16 digits , if we calculate and try 10^5 per second , it will cost 10^15/(365*24*60*60)/10^5=317.1years for us to find this factor , Peter Strasser found this factor of F118, and F118 approximate has 10^35digits , so it is impossible to find this factor by ECM . who can tell me how to find this factor of F118 F118=2^(2^118)+1 http://www.prothsearch.com/fermat.html 
20201105, 05:52  #2  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·17·139 Posts 
Quote:
Peter Strasser searched really hard with software shown here and found this factor of F118, and that's the end of this story. It says it right there  he found it with mmff. That means  using a GPU. Now, how did I find this one? Quote:


20201105, 06:23  #3  
Feb 2019
China
59 Posts 
Quote:
I have no GPU ,I only have CPU 

20201105, 06:34  #4 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
5·41·47 Posts 

20201105, 09:01  #5  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×17×139 Posts 
Quote:
What if there is no factor of F118 to be found with this century's technology? Then you can set up your program on a hundred computers, press some buttons and wait for a 100 years and nothing will be found  because it isn't there. Maybe the next factor of F118 is (a 49digit number)*2^120 + 1. Or maybe (a 79digit number)*2^120 + 1, then what? 

20201105, 10:33  #6 
Romulan Interpreter
Jun 2011
Thailand
2×3^{2}×23^{2} Posts 

20201105, 13:05  #7 
Feb 2017
Nowhere
11E2_{16} Posts 
Things any doityourselfers should keep in mind
Ask yourself, "Do I really want to do this myself?" If you're sure... 1) Understand the job you are trying to do 2) Know the techniques for doing it 3) Get (borrow, rent, buy) good tools and equipment 4) Make sure you know how to use them Now, I'm unlikely to go searching for factors of Fermat numbers myself. Even so, I believe I can understand (1) and, to some degree, (2) for this task. So when I see a new announcement, I can have some appreciation of the hard work that went into making it happen. The Fermat numbers being looked at are so large, about the only plausible way to find factors is to search through "small" candidates and hope you get lucky. About all I know in this regard is that, for n > 1, all factors of F_{n} are congruent to 1 (mod 2^{n+2}). So you look at N = k*2^{n+2} + 1 and see whether N divides F_{n}. This would involve repeated squaring starting with Mod(2, N). At this point, I ask myself, "Is it worthwhile to weed out Nvalues with small prime factors to avoid doing this test on them?" My guess is, "Seems pretty likely." So, I'm guessing you need something that can do some fast sieving, and something that can handle repeated squarings (mod N) for largishtolarge N quickly. If I were seriously interested in trying it myself, I would inquire further into what the right tools for the job might be, and how I can get the use of them within my budget. The regular contributors to the various forums and threads devoted to specific factoring efforts know this stuff as well as anyone on the planet. I'm sure they would be more than happy to help someone who asks respectfully. Part of that respect is IMO putting some effort of your own into learning (1) and (2) above before seeking help. Just my 
20201105, 13:14  #8 
Mar 2019
2×5×17 Posts 
The FermatSearch website is a reasonably good starting point; it has links to lots of software you can download, information about which ones are good for which ranges, FAQ, lists of available ranges, etc.
Good luck! 
20201105, 13:19  #9  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
31×199 Posts 
Quote:
I'd like add one more: 5) Learn what has already been searched and don't waste time redoing the same work. 

20201105, 13:40  #10 
"Mike"
Aug 2002
8,191 Posts 

20201105, 14:40  #11  
Feb 2017
Nowhere
2·3·7·109 Posts 
Quote:
I remember something I did when I was 5 or 6 years old. I had gotten up and dressed. I happened to look where I always put my glasses when I went to bed. They weren't there! I looked on the floor nearby. No glasses. I thought, "Where else do I set them down?" So I looked in the bathroom, by the washbowl, since I cleaned them there. My dad was shaving. He asked me what I was doing. I told him I was looking for my glasses. He got kind of a funny smile on his face. I looked in a few other places. I went back to Dad, to ask him if he knew where my glasses were. But before I could ask, I saw my face in the mirror. And I knew where my glasses were. So, yes, I can say from experience that it is a good idea to make sure you're not trying to find something that is already found. I don't remember recent things so well, of course... 

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