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Old 2018-08-08, 08:10   #265
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Quote:
Originally Posted by R. Gerbicz View Post
Just interestingly, if m=k*2^(n+2)+1 | F_n (where k can be even) and 0<k<2^(n+2) then m is prime! And this holds for the known factors in the list (surely) for say n>100.
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
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Old 2018-08-08, 08:19   #266
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Quote:
Originally Posted by GP2 View Post
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 View Post
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
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Old 2018-08-08, 08:35   #267
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Quote:
Originally Posted by ATH View Post
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
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Old 2018-08-08, 13:37   #268
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Quote:
Originally Posted by Batalov View Post
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...

Running the precompiled statically-linked version pfgw64s made no difference.


I'm a bit alarmed for Gary though...
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Old 2018-08-08, 13:44   #269
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Quote:
Originally Posted by GP2 View Post
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.
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Old 2018-08-08, 16:02   #270
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Actually according to your table, the cutover from using pfms to gfndsieve+pfgw is around n = 5000.
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Old 2018-08-08, 16:06   #271
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Quote:
Originally Posted by rogue View Post
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
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Old 2018-11-02, 02:30   #272
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Default 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.
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Old 2018-11-02, 10:40   #273
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Quote:
Originally Posted by Gary View Post
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!
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Old 2018-12-19, 04:01   #274
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Default 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
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Old 2018-12-20, 12:13   #275
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Default 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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