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2018-08-08, 08:10   #265
GP2

Sep 2003

2,579 Posts

Quote:
 Originally Posted by R. Gerbicz Just interestingly, if m=k*2^(n+2)+1 | F_n (where k can be even) and 0100.
Among the currently known factors, the largest n for which it the above condition 0<k<2^(n+2) fails (k can be even) is:

42 45 111318179143061

Last fiddled with by GP2 on 2018-08-08 at 08:37

2018-08-08, 08:19   #266
ATH
Einyen

Dec 2003
Denmark

3×5×193 Posts

Quote:
 Originally Posted by GP2 Maybe you could use pfgw to verify that the known Fermat factors really are prime factors and not composite factors? But maybe not for the goal I wanted. Or am I misunderstanding?
Looking in the pfgwdoc.txt for -gos2 it does test the Fermat factors without testing primality.

Quote:
 -g Generalized Fermat factor testing The complete syntax is: -g[x][o][s][q]{#,#}{#,#}[_dump_search_patterns] Also allowed is -g[o][q]# and -gx[o][q]#,# to test single GF (or xGF) number This will test the numbers to see if they divide any fermat number. All prp's or primes (N-1 only) which are in the correct form of being a Fermat factor will go through the test. o: The o is needed when you only want to test for Fermat factors, and NOT test the numbers for probable primality. ([O]nly perform GF divisibility). s: The s is an 'undocumented' feature, which saves the residue of each b^(2^(n-1)) into a file, so that a re-run of the number will be much quicker. (CAUTION here, this function does NOT delete the files, so things can add up quickly). The -g (or -go) may be followed by the GF base you wish to check for. if no base is entered, then the default will be -g[o]{2,5}{2,12} So -go2 will ONLY check (no prp) for Fermat divisors of base 2. Ranges of bases can also be entered. The format is:
Quote:
 Originally Posted by GP2 Among the currently known factors, the largest n for which it fails is: 42 45 111318179143061
It does not fail? 111318179143061*2^45+1 = 222636358286122*2^44+1 is prime.

I just tested pfgw on this factor, you just have to write the factor as 111318179143061*2^45+1 in a text file.
111318179143061*2^45+1 is a Factor of F42!!!! (0.000000 seconds)

Last fiddled with by ATH on 2018-08-08 at 08:25

2018-08-08, 08:35   #267
GP2

Sep 2003

2,579 Posts

Quote:
 Originally Posted by ATH It does not fail? 111318179143061*2^45+1 = 222636358286122*2^44+1 is prime.
No, I meant it fails the condition of:

0<K<2^(n+2)

where unlike the usual "k", this K can be even, i.e., K = 2^(m-(n+2)) * k

I edited my previous post to make this clear.

Last fiddled with by GP2 on 2018-08-08 at 08:37

2018-08-08, 13:37   #268
GP2

Sep 2003

257910 Posts

Quote:
 Originally Posted by Batalov Try on the same platform and compare times: 1. download pfgw 2. put all factors in a file 3. run pfgw -N -k -l -gos2 file
I downloaded pfgw from Sourceforge, with precompiled executable pfgw64, it's version 3.8.3_20170121

I ran it on a c5d.large instance on AWS (one core, Skylake, 3.0 GHz Xeon), same platform as for the GMP program.

Here are the times:

Code:
7905*2^352281+1 is a Factor of F352279!!!! (39.253506 seconds)
vs. my GMP program = 957 sec (24 times slower)

11*2^960901+1 is a Factor of F960897!!!! (219.145612 seconds)
vs. my GMP program = 7587 sec (35 times slower)
vs. Gary pmfs = 47 minutes = 2820 sec (13 times slower) running on unknown system

193*2^3329782+1 is a Factor of F3329780!!!! (3428.316006 seconds)
vs. my GMP program = 124205 sec (36 times slower)
Very impressive.

It's amusing that pfgw gives times to the millionth of a second...

I'm a bit alarmed for Gary though...

2018-08-08, 13:44   #269
ET_
Banned

"Luigi"
Aug 2002
Team Italia

112338 Posts

Quote:
 Originally Posted by GP2 I downloaded pfgw from Sourceforge, with precompiled executable pfgw64, it's version 3.8.3_20170121 I ran it on a c5d.large instance on AWS (one core, Skylake, 3.0 GHz Xeon), same platform as for the GMP program. Here are the times: Code: 7905*2^352281+1 is a Factor of F352279!!!! (39.253506 seconds) vs. my GMP program = 957 sec (24 times slower) 11*2^960901+1 is a Factor of F960897!!!! (219.145612 seconds) vs. my GMP program = 7587 sec (35 times slower) vs. Gary pmfs = 47 minutes = 2820 sec (13 times slower) running on unknown system 193*2^3329782+1 is a Factor of F3329780!!!! (3428.316006 seconds) vs. my GMP program = 124205 sec (36 times slower) Very impressive. It's amusing that pfgw gives times to the millionth of a second... Running the precompiled statically-linked version pfgw64s made no difference. I'm a bit alarmed for Gary though...
Don't

PMFS is quite impressive for N below 30,000.

 2018-08-08, 16:02 #270 rogue     "Mark" Apr 2003 Between here and the 2×29×101 Posts Actually according to your table, the cutover from using pfms to gfndsieve+pfgw is around n = 5000.
2018-08-08, 16:06   #271
ET_
Banned

"Luigi"
Aug 2002
Team Italia

11×433 Posts

Quote:
 Originally Posted by rogue Actually according to your table, the cutover from using pfms to gfndsieve+pfgw is around n = 5000.
Sure, but pmfs can make great use of threads ;-)

Last fiddled with by ET_ on 2018-08-08 at 16:06

 2018-11-02, 02:30 #272 Gary     "Gary" Aug 2015 Texas 608 Posts A new factor from FermatSearch I would like to report the following new Fermat factor: ***** 19,789,270,693 * 2^2148 + 1 divides F2144 This was discovered today running pmfs on my Superdome X system.
2018-11-02, 10:40   #273
ET_
Banned

"Luigi"
Aug 2002
Team Italia

11·433 Posts

Quote:
 Originally Posted by Gary I would like to report the following new Fermat factor: ***** 19,789,270,693 * 2^2148 + 1 divides F2144 This was discovered today running pmfs on my Superdome X system.
Congratulations Gary!

 2018-12-19, 04:01 #274 Gary     "Gary" Aug 2015 Texas 4810 Posts One more new factor for 2018 from FermatSearch I am happy to report the following new Fermat factor: ***** 6,604,326,057 * 2^3347 + 1 divides F3345 This was discovered on Dec 13 running pmfs on my HPE Superdome X system. Wishing everyone a joyous holiday season and a Happy New Year! Last fiddled with by Gary on 2018-12-19 at 04:33
 2018-12-20, 12:13 #275 ET_ Banned     "Luigi" Aug 2002 Team Italia 11·433 Posts Two in 6 days! December 19th, 2018 New Fermat factor from FermatSearch! 1075441212722595 . 2135+1 is a Factor of F132!!! Peter Strasser discovered the seventh Fermat factor of this year! He used George Woltman's mmff program running on his home computer. Congratulations to Peter from FermatSearch, for his second factor! Moderators please modify the title: Gostin factor was found on Dec. 13th. - Last fiddled with by ET_ on 2018-12-21 at 08:43

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