2014-11-19, 10:11 | #1 |
Dec 2010
2·37 Posts |
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? |
2014-11-19, 10:20 | #2 |
Sep 2002
Database er0rr
2^{2}×883 Posts |
Put the Mersenne in a "helper file":
Code:
$ cat > helper.txt 2^3217-1 Code:
$ ./pfgw64 -t -hhelper.txt -q"1816*(2^3217-1)+1" PFGW Version 3.7.7.64BIT.20130722.x86_Dev [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 |
2014-11-19, 10:24 | #3 |
Romulan Interpreter
Jun 2011
Thailand
9150_{10} 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 Code:
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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