New Generalized Fermat factors

[Batalov]

Embarassingly easily, I have found a factor for F_20(6)
http://www1.uni-hamburg.de/RRZ/W.Keller/GFN06.html

P-1 found a factor in stage #2, B1=100000, B2=10000000, E=12.
6^1048576+1 has a factor: 522767209448794182647809
k = 124637415277670427, N=22

(No previously known factors.)

It is possible that the new Prime95 binary preloads the group order with a necessary amount of "2"s, maybe?

[axn]

Originally Posted by Batalov

It is possible that the new Prime95 binary preloads the group order with a necessary amount of "2"s, maybe?

Unlikely. 27.6 (the latest source that I have) doesn't do so. You probably just lucked out.

[Batalov]

It looks easier to find than other (e.g. G.Reynolds') factors.
The cofactor is surely composite but I am running a 5-PRP test just in case on a slow computer.

I've tested my luck on m=3,5,6,8,10,12; 17<=N<=24 and found nothing else so far.
I was actually building a chimera of mmff and mfaktc-repunit (c) Danilo MrRepunit; ran P-1 on Gfn_20(6) just out of boredom. Imagine my surprize. ;-)

W.Keller didn't respond yet.

[axn]

Originally Posted by Batalov

I've tested my luck on m=3,5,6,8,10,12; 17<=N<=24 and found nothing else so far.

Could be because of the missing pre-loading thingie. How about you hack the source of prime95 and build your own (you don't need to talk to primenet, so security code and such are not needed).

If you're serious about running big P-1 job on GFNs, then porting P-1 algorithm using Genefer FFT routines might be the way to go (will be useful for the Prime Grid searches as well). [Easier said than done ]

[Batalov]

Yep, "we can rebuild him! We have the technology!"
I had built it with modifications before.

I am more interested to make the mmff-GFN work first though. (Not much hassle, just some preinits to be rewritten and the classes redefined. And of course N>=m+1, not 2)

[ET_]

Originally Posted by Batalov

Yep, "we can rebuild him! We have the technology!"
I had built it with modifications before.

I am more interested to make the mmff-GFN work first though. (Not much hassle, just some preinits to be rewritten and the classes redefined. And of course N>=m+1, not 2)

I'd be interested in such program as well...
Do you plan to integrate xGF also?

Luigi

[Batalov]

Axn, you are right, it is still not preloaded in 27.7 neither:

ecm.c:line ~4560

/* For Mersenne numbers, 2^n-1, make sure we include 2n in the calculated */
/* exponent (since factors are of the form 2kn+1).  For (Generalized) Fermat numbers, */
/* [COLOR=red]2[/COLOR] B^n+1 (n is a power of 2), make sure the exponent is included in the */
/* calculated exponent as factors are of the form kn+1.  Otherwise, do */
/* nothing special -- start with one. */
        if (lower == 0 && k == 1.0 && b == 2 && c == -1) itog (2*n, g);
        else if (lower == 0 && k == 1.0 && [COLOR=red]b == 2 &&[/COLOR] c == 1) itog (n, g);
        else setone (g);

[Batalov]

P.S. For Fermat (b=2), g should be rather 4n, and for GNF (b>2), 2n.
But even n would do the trick already.

I do remember this bit of code having already been discussed on the forum years ago.

[axn]

Originally Posted by Batalov

P.S. For Fermat (b=2), g should be rather 4n, and for GNF (b>2), 2n.
But even n would do the trick already.

I do remember this bit of code having already been discussed on the forum years ago.

For one such discussion, go to my profile and find all threads started by me. Third one should do the trick

My preferred solution is to _always_ throw in n (or 4n) in there, regardless of the form of the number.

[Batalov]

I found a lived-in old (26.6) code that I had used for tests on linux64. That's less hassle than try to get VStudio and curl and everything and start anew on my new Win64 machine (old one is gone).

The vanilla mprime didn't find some easy factors for GFN(6), m=18,19...
The patched one found the easy ones (as could have been expected) in Step 1.

Now, I'll load some reruns for m=3,5,6,8,10,12 and go to sleep. Harvest in the morning.

The F_20(6) factor is genuine, though. The cofactor is composite.

[Prime95]

Originally Posted by axn

My preferred solution is to _always_ throw in n (or 4n) in there, regardless of the form of the number.

Fixed in 27.8 or 28.1 whichever is released next. I'll always throw in 2n.