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Old 2014-11-19, 10:11   #1
Dec 2010

2·37 Posts
Default How can I prove this PRP prime?

According to PFGW, 1816 x (2^3217 - 1) + 1 is a PRP.

(FYI: 2^3217 - 1 is a Mersenne prime.)

I thought PFGW would use Pocklington's test as N-1 is easy to completely factor.

Am I missing a switch in PFGW?
Is there an alternative to Pocklington's test?
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Old 2014-11-19, 10:20   #2
paulunderwood's Avatar
Sep 2002
Database er0rr

5·787 Posts

Put the Mersenne in a "helper file":

$ cat > helper.txt
$ ./pfgw64 -t -hhelper.txt -q"1816*(2^3217-1)+1"
PFGW Version [GWNUM 27.11]

Primality testing 1816*(2^3217-1)+1 [N-1, Brillhart-Lehmer-Selfridge]                                    
Reading factors from helper file helper.txt
Running N-1 test using base 3                                                  
Calling Brillhart-Lehmer-Selfridge with factored part 99.66%
1816*(2^3217-1)+1 is prime! (0.0244s+0.0037s)

Last fiddled with by paulunderwood on 2014-11-19 at 10:22
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Old 2014-11-19, 10:24   #3
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Jun 2011

24×613 Posts

You have to create a helper file, call it "m18.prm" (the name and extension totally up to you) and write inside a single line "2^3217-1", without quotes, and followed by an enter (carriage return).
Then you make a worktodo file, call it work_18.txt, or whatever, in which you put the work to do (it is an ABC2 file, etc).
Then launch pwgw with something like

pfgw64 -t -lmm_18.log -hm18.prm work_18.txt

PFGW doesn't know that M18 is prime, he can't do LL tests. You have to specify this in -h file and he'll trust you.

Last fiddled with by LaurV on 2014-11-19 at 10:25
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