mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Factoring

Reply
 
Thread Tools
Old 2012-09-18, 19:01   #1
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22·2,281 Posts
Default New Generalized Fermat factors

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?
Batalov is offline   Reply With Quote
Old 2012-09-19, 04:20   #2
axn
 
axn's Avatar
 
Jun 2003

13·192 Posts
Default

Quote:
Originally Posted by Batalov View Post
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.
axn is offline   Reply With Quote
Old 2012-09-19, 04:42   #3
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22×2,281 Posts
Default

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.
Batalov is offline   Reply With Quote
Old 2012-09-19, 06:34   #4
axn
 
axn's Avatar
 
Jun 2003

469310 Posts
Default

Quote:
Originally Posted by Batalov View Post
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 ]
axn is offline   Reply With Quote
Old 2012-09-19, 07:02   #5
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22×2,281 Posts
Default

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)
Batalov is offline   Reply With Quote
Old 2012-09-19, 08:08   #6
ET_
Banned
 
ET_'s Avatar
 
"Luigi"
Aug 2002
Team Italia

2·2,383 Posts
Default

Quote:
Originally Posted by Batalov View Post
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

Last fiddled with by ET_ on 2012-09-19 at 08:09
ET_ is offline   Reply With Quote
Old 2012-09-19, 09:25   #7
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22·2,281 Posts
Default

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

ecm.c:line ~4560
Code:
/* 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 is offline   Reply With Quote
Old 2012-09-19, 09:30   #8
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22·2,281 Posts
Default

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.
Batalov is offline   Reply With Quote
Old 2012-09-19, 09:45   #9
axn
 
axn's Avatar
 
Jun 2003

13×192 Posts
Default

Quote:
Originally Posted by Batalov View Post
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.

Last fiddled with by axn on 2012-09-19 at 09:45 Reason: once -> one
axn is offline   Reply With Quote
Old 2012-09-19, 10:36   #10
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22·2,281 Posts
Default

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.
Batalov is offline   Reply With Quote
Old 2012-09-19, 19:37   #11
Prime95
P90 years forever!
 
Prime95's Avatar
 
Aug 2002
Yeehaw, FL

7·1,021 Posts
Default

Quote:
Originally Posted by axn View Post
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.
Prime95 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Generalized Fermat numbers (in our case primes) pepi37 Conjectures 'R Us 4 2015-10-09 14:49
Pseudoprimality Hypothesis for Specific Class of Generalized Fermat Numbers primus Miscellaneous Math 1 2015-03-25 22:18
Generalized Fermat factors - why? siegert81 Factoring 1 2011-09-05 23:00
Generalized Fermat Numbers ET_ Programming 4 2008-06-23 07:59
Generalized Fermat Prime Search? pacionet Lounge 3 2006-01-25 15:40

All times are UTC. The time now is 09:40.

Sat Sep 19 09:40:56 UTC 2020 up 9 days, 6:51, 0 users, load averages: 1.40, 1.48, 1.61

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.