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Old 2012-10-12, 03:53   #1
Batalov
 
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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
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Old 2012-10-12, 03:57   #2
Batalov
 
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Default Reservations for GFN3

Available ranges:
N=25-31 | k from 1500e12
N=32-50 | k from 100e12
N=51-70 | k from 40e12
N=71-100 | k from 20e12
N=101-144 | k from 10e12
N=145-178 | k from 4e12
N=179-208 | k from 2.199e12

N=209-223 | _done_ to 252 bits

Reservations:
-

Last fiddled with by Batalov on 2016-03-06 at 07:27
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Old 2012-10-12, 03:57   #3
Batalov
 
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Default Reservations for GFN5

Available ranges:
N=25-32 | k from 200e12
N=33-35 | k from 150e12
N=36-48 | k from 70e12
N=49-67 | k from 20e12
N=68-176 | k from 10e12
N=177 | k from 8.69e12
N=178 | k from 4.398e12
N=179
-209 | k from 2.199e12
N=210-223 | _done_ to 252 bits

Reservations:
-

Last fiddled with by Batalov on 2016-03-08 at 05:30
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Old 2012-10-12, 03:57   #4
Prime95
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Quote:
Originally Posted by Batalov View Post
You would then report factors to W.Keller as "I.Surname & Woltman"
I.M.O. Oliver Weihe also deserves credit. mmff would not exist without Oliver's mfaktc work. Similarly, one Batalov deserves some programming credit too.
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Old 2012-10-12, 03:57   #5
Batalov
 
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Default Reservations for GFN6

Available ranges:
N=25-29 | k from 2000e12
N=30-49 | k from 1200e12
N=50-69 | k from 300e12
N=70-90 | k from 200e12
N=91-100 | k from 100e12
N=101-143 | k from 35e12
N=144-160 | k from 20e12
N=161-177 | k from 6e12
N=178 | k from 4.398e12
N=179-210 | k from 2.199e12

N=211-223 | _done_ to 252 bits

Reservations:
-

Last fiddled with by Batalov on 2015-02-06 at 18:12
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Old 2012-10-12, 03:57   #6
Batalov
 
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Default Reservations for GFN7

Available ranges:
N=25 | k from 10e12
N=26-29 | k from 80e12
N=30-34 | k from 50e12
N=35-39 | k from 38e12
N=40-46 | k from 28e12
N=47-50 | k from 17.59e12
N=51-100 | k from 3e12
N=101-200 | k from 2e12
N=201-211 | k from 1e12

N=212-223 | _done_ to 252 bits

Reservations:
N=26-50 | k from 2e12 to 17.59e12 Batalov
N=51-100 | k from 2e12 to 3e12 Batalov
N=101-200 | k from 1e11 to 2e12 Batalov

Last fiddled with by Batalov on 2016-11-07 at 23:23
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Old 2012-10-12, 03:58   #7
Batalov
 
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Default Reservations for GFN10

Available ranges:
N=25-31 | k from 200e12
N=32-39 | k from 300e12
N=40-49 | k from 100e12
N=50-99 | k from 35e12
N=100-144 | k from 10e12
N=145-209 | k from 6e12
N=210-223 | _done_ to 252 bits

Reservations:
N=32-39 | k from 200e12 to 300e12 S.B.

Last fiddled with by Batalov on 2016-03-01 at 10:24
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Old 2012-10-12, 03:58   #8
Batalov
 
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Default Reservations for GFN11

Available ranges:
N=25-50 | k from 2e12
N=51-100 | k from 1e12
N=101-200 | k from 3e11
N=201-211 | k from 1e12

N=212-223 | _done_ to 252 bits

Reservations:
-

Last fiddled with by Batalov on 2016-11-05 at 16:38
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Old 2012-10-12, 03:59   #9
Batalov
 
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Default Reservations for GFN12

Available ranges:
N=25 | k from 100e12
N=26-29 | k from 200e12
N=30-32 | k from 150e12
N=33-39 | k from 100e12
N=40-52 | k from 50e12
N=53-63 | k from 30e12
N=64-79 | k from 20e12
N=80-100 | k from 10e12
N=101 | k from 200e12
N=102-110 | k from 281.474e12
N=111-141 | k from 140.737e12
N=142 | k from 70.368e12
N=143 | k from 35.184e12
N=144 | k from 17.592e12
N=145 | k from 8.796e12
N=146-177 | k from 6e12
N=178-200 | k from 1.099e12
N=201 | k from 2e12
N=202-209 | k from 1.099e12

N=210-223 | _done_ to 252 bits

Reservations:
-

Last fiddled with by Batalov on 2014-06-27 at 01:09
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Old 2012-10-12, 04:19   #10
Batalov
 
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The speed of mmff-gfn is similar to mmff, but roughly a chunk 4e12-10e12 for some N~=70 is probably ~ 1 hour on GTX570, and a chunk 2e12-10e12 for some N~=120 is maybe a few hours. So you may want to take them by N ranges of multiples of 10 easily.

It would be nice to take everything initially to k<=10e12. Remember, the success probability* is ~ 1/kN * O(some pesky logs), so you may probably want the low k's.

____
*per unit of time! ... or even ~ 1/kN2

Last fiddled with by Batalov on 2012-10-16 at 06:08 Reason: (footnote)
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Old 2012-10-12, 04:55   #11
LaurV
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Waiting for a win64 binary and then I may invest some time (like a week or so) and few gtx580 into one or more of those ranges. As you might already noticed, I like to try a bit of everything and this should be my opportunity to tickle the GFN domain. Unfortunately, no time to play with building win64 executables now (I succeeded to compile CL in the past, but never played with mfaktc, though the process would be somehow straight forward).
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