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Batalov 2012-10-12 03:53

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 [URL=""]posted here[/URL]) - and have fun!

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

Is anyone interested?

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

[COLOR=green]For Windows, get the and 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.[/COLOR]

[COLOR=green]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; [I]and[/I] you will need [/COLOR]

[COLOR=#008000]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). [/COLOR]

[COLOR=blue]If you find a factor, you can validate it before getting too excited - in a few ways:[/COLOR]
[COLOR=blue]1. paste in [URL=""]factorDB[/URL]. It should be prime or PRP. [SIZE=1]If it is composite, then both small factors are very likely to be already known.[/SIZE][/COLOR]
[SIZE=1][COLOR=#0000ff]Example: "GF(23,5) has a factor: 3680510522410915594241" (which is = 167772161 * [/COLOR][/SIZE][SIZE=1][COLOR=#0000ff]21937552097281); a pair of valid, known factors
[COLOR=blue]2. Using factorDB (or Pari, or even bc -l or dc) get the canonical form [B]k[/B]*2^[B]N[/B]+1 and then run [FONT=Franklin Gothic Medium][B]pfgw -f -gxo -q"k*2^N+1[COLOR=blue]". [/COLOR][/B][/FONT][/COLOR][COLOR=blue]Expect a message with four exclamation points.[/COLOR]
[COLOR=blue]3. Using Pari/GP, you can run [B][FONT=Franklin Gothic Medium]Mod(b,f)^(2^m)+1[/FONT][/B] (and expect a 0)[/COLOR]

Batalov 2012-10-12 03:57

Reservations for GFN3
[COLOR=green]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[/COLOR]
N=209-223 | _done_ to 252 bits


Batalov 2012-10-12 03:57

Reservations for GFN5
[COLOR=green]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[/COLOR][COLOR=green][COLOR=green]-209[/COLOR] | k from 2.199e12
[/COLOR]N=210-223 | _done_ to 252 bits


Prime95 2012-10-12 03:57

You would then report factors to W.Keller as "I.Surname & Woltman" [/QUOTE]

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.

Batalov 2012-10-12 03:57

Reservations for GFN6
[COLOR=green]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[/COLOR]
N=211-223 | _done_ to 252 bits


Batalov 2012-10-12 03:57

Reservations for GFN7
[COLOR=green]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[/COLOR]
N=212-223 | _done_ to 252 bits

[COLOR=Red]N=26-50 | k from 2e12 to 17.59e12 Batalov[/COLOR]
[COLOR=Red]N=51-100 | k from 2e12 to 3e12 Batalov[/COLOR]
[COLOR=Red]N=101-200 | k from 1e11 to 2e12 Batalov[/COLOR]

Batalov 2012-10-12 03:58

Reservations for GFN10
[COLOR=green]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
[/COLOR]N=210-223 | _done_ to 252 bits

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

Batalov 2012-10-12 03:58

Reservations for GFN11
[COLOR=green]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[/COLOR]
N=212-223 | _done_ to 252 bits


Batalov 2012-10-12 03:59

Reservations for GFN12
[COLOR=green]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[/COLOR]
N=210-223 | _done_ to 252 bits


Batalov 2012-10-12 04:19

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[COLOR=darkred]*[/COLOR] is ~ 1/kN * O(some pesky logs), so you may probably want the low k's.

[COLOR=darkred]*[/COLOR]per unit of time! ... or even ~ 1/kN[sup]2[/sup]

LaurV 2012-10-12 04:55

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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