View Single Post
Old 2012-10-12, 03:53   #1
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

32×17×61 Posts
Cool GFN factoring with mmff-gfn | Reservations

Is anyone hungry for factors?

I was and I now have satisfied my initial thirst and would like to put my GPUs back into Fermat only. GFN (Generalized Fermat numbers) will give you a needed break from proper Fermats!

So, I wanted to help out by maintaining a reservation thread. I will post all open ranges (and mark my words, there are factors in 'em!) and you could take a range (and a base), get the binary (flashjh built Windows binaries which are posted here) - and have fun!

You would then report factors to W.Keller as "I.Surname & Woltman" (absence of initial means the program author) and here in the GFN factors thread.

Is anyone interested?

For either Win/Linux, get the tests_and_cudart.zip file. Unzip.
Use separate folders for each base. Use sample worktodo.txt files from the tests_and_cudart.zip file. Put the library and mmff.ini in each folder.

For Windows, get the mmff-gfnX-0.26-win32-win64.zip and tests_and_cudart.zip files. Put the library, mmff.ini and the corresponding EXE file in each folder and start by running sample on the worktodo.txt file. Inspect the results.txt files.

For Linux, you will be better off building your own binary (source is posted, too), but you can try the posted binaries (they were built in OpenSuSE, so they may not work for you; and you will need libcudart.so).

Note that for N<=25, the limits are k>=10e12 already and furthermore that range of N has been already bombarded with P-1 and ECM. The useful range for mmff-gfn starts approximately from N>=26, where the previous search limits were 2e12 (N<=50), 1e12 (N<=100) and 0.1e12 (N>100).
_______________________


If you find a factor, you can validate it before getting too excited - in a few ways:

1. paste in factorDB. It should be prime or PRP. If it is composite, then both small factors are very likely to be already known.
Example: "GF(23,5) has a factor: 3680510522410915594241" (which is = 167772161 * 21937552097281); a pair of valid, known factors

2. Using factorDB (or Pari, or even bc -l or dc) get the canonical form k*2^N+1 and then run pfgw -f -gxo -q"k*2^N+1". Expect a message with four exclamation points.

3. Using Pari/GP, you can run Mod(b,f)^(2^m)+1 (and expect a 0)

Last fiddled with by Batalov on 2012-10-13 at 09:31
Batalov is offline   Reply With Quote