2^9092392+40291 is a probable prime!

[philmoore]

Originally Posted by enderak

Phil, my double-check was done on an Intel i7 965 running on all 4 cores at once. If you can give me direction I would be happy to help with the pfgw tests. (Running 64-bit Windows OS)

Should I run it per mdettweiler's suggestion or can you e-mail your script file with directions to use? If the various tests can be split up, I have a few i7's available that could greatly reduce the test time. (Who ever said that patience is a virtue?)

I was wondering how you ran that test so quickly!

I'll post a script file tomorrow and you can try it out. I really don't mind running the tests, and I really think that by the time we get three or four confirming results, we can assume that everything is good, but you may enjoy doing something different for a change, now that we are so close to the end of this project.

The problem with Max's suggestion is that according to my understanding, pfgw will use a few bases, and not necessarily the ones that we might choose. Let's try the script file.

Double-checking is a low priority, but since the queue is already set up, should I ask John Blazek if the PRPNET queue can be activated?

[ATH]

Originally Posted by mdettweiler

pfgw -tc -q2^9092392+40291

That will perform a combined N-1/N+1 primality test, which of course will not totally succeed since neither N-1 or N+1 can be trivially factored, but the test still produces strong Fermat and Lucas PRP verification.

Where does it say about strong Fermat and Lucas PRP verification?

-tc Combined N+1 and N-1 test.
When you are short of factoring N-1, or N+1, and the other
has some factors, you can try this mode to achieve a prove.
This too is NOT a probable test.
If the factored portions are F1 and F2, with F1>F2, and 3*F1+F2 is
100% or more, pfgw will be able to complete the proof. If this total
is slightly below 100%, it should still be able to force a proof
with some square tests using the -x flag.

[akruppa]

Another factor: 76727594460993167.

[philmoore]

I think Max (mdettweiler) is right, and this is worth a try. His suggestion was to run it with:
pfgw -tc -q2^9092392+40291
I'm thinking that maybe
pfgw -tc -l -q2^9092392+40291
will log the output. Report what bases it uses for the strong prp tests, and I'll remove them from my queue.

[philmoore]

Here is a version of the script file:

SCRIPT
DIMS Blankline,
DIMS Residup1, Probable_prime_residueis_plus1
DIMS Residum1, Probable_prime_residueis_minus1
DIMS Resultfails, Fails_test
DIM Base
DIM Result
DIM Resultres

SET Base,2
PRINT Base
POWMOD Result,Base,2^9092391+20145,2^9092392+40291
SET Resultres,(Result+1)%(2^9092392+40291)
IF (Resultres==0) THEN PRINT Residum1
IF (Resultres==0) THEN GOTO End_test
IF (Resultres==2) THEN PRINT Residup1
IF (Resultres==2) THEN GOTO End_test
SET Resultres,Resultres%(2^64)
PRINT Resultfails
PRINT Resultres
LABEL End_test
PRINT Blankline

END

Change the base from 2 to something else, save the file as, say, strongtest.txt, then run the test in pfgw with the command line "pfgw strongtest.txt -l". The -l flag will log the output to pfgw.out. For other Five or Bust finds in the past, we have run tests with all prime bases from 2 to 71. I have already queued up 2, 3, 5, and 7, so if you want to try this, post which bases you are testing below. You could modify this script file to run several bases sequentially.

The Jacobi symbol predicts whether we should find a residue of +1 or -1. The message "Fails_test" means, if that result can be verified, that the number is actually composite.

[Jeff Gilchrist]

I will take 11, 13, 17, 19, 23, 29

[enderak]

I'm thinking that maybe
pfgw -tc -l -q2^9092392+40291
will log the output. Report what bases it uses for the strong prp tests, and I'll remove them from my queue.

OK, I am running this now.

[Batalov]

Originally Posted by enderak

OK, I am running this now.

Put Alex's factors in a file, say, helperPRPm1 and run
pfgw -f1 -e999999 -tc -hhelperPRPm1 -l -q"2^9092392+40291"

There's no way to enforce the base though.
You can also add -e999999 (even less factoring) and there was some other flag that overrides the reporting frequency from 2500 iterations (but for this number it is good enough).

It appears that the first tried base will be 2 for N-1 and 1+sqrt(5) for N+1 but later the program may do other bases -- you will see.

[enderak]

OK, have done this. Thanks for the help - as you can tell I am new to pfgw

[philmoore]

Serge's suggestion will save you from repeating the factoring. Thanks!

[engracio]

Just thought I might pile on some more on this prime. I have completed the rerun on a different computer. DUH!!! It's still a prime.

Also completed/submitted my part of wu lower than the prime to Phil.