## Unable to prove a PRP

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• How can one prove the primality of a PRP when every program I ve tried is unable. To form of the prime is XYYX such as 2^2007+2007^2. I have many PRP s to
Message 1 of 4 , Dec 12, 2006
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How can one prove the primality of a PRP when every program I've tried
is unable. To form of the prime is XYYX such as 2^2007+2007^2. I have
many PRP's to check with the smallest being around 10k digits. Primo
cannot handle the numbers and PFGW stops and complains that there are
not enough factors. The switches, -t, -tp, -tc and -tm will not
complete the proof. I've tried gmp-ecm and it seems like it'll take a
few thousand years to run all the curves searching for factors. Anyone
have any ideas?
• ... With a little less than 30% factorisation of N+1 and N-1 you can get a *proof* of primailty using PFGW plus CHG [1]. Otherwise a parallel implementation of
Message 2 of 4 , Dec 12, 2006
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--- In primenumbers@yahoogroups.com, "Bryan" <beyastard@...> wrote:
>
> How can one prove the primality of a PRP when every program I've tried
> is unable. To form of the prime is XYYX such as 2^2007+2007^2. I have
> many PRP's to check with the smallest being around 10k digits. Primo
> cannot handle the numbers and PFGW stops and complains that there are
> not enough factors. The switches, -t, -tp, -tc and -tm will not
> complete the proof. I've tried gmp-ecm and it seems like it'll take a
> few thousand years to run all the curves searching for factors. Anyone
> have any ideas?
>

With a little less than 30% factorisation of N+1 and N-1 you can get a
*proof* of primailty using PFGW plus CHG [1]. Otherwise a parallel
implementation of ECPP such as FastECPP [2] would do, given you had
the code and several networked computers,

[1] http://tech.groups.yahoo.com/group/primeform/files/
[2] http://primes.utm.edu/bios/page.php?id=689

Can you tell us what the numbers are and how much factorisation of
these you have achieved todate?

Paul
• ... It looks like you could be rehashing stuff that s already been done: http://www.leyland.vispa.com/numth/primes/xyyx.htm Are you aware of that web page? A
Message 3 of 4 , Dec 12, 2006
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--- In primenumbers@yahoogroups.com, "Bryan" <beyastard@...> wrote:
>
> How can one prove the primality of a PRP when every program I've
> tried is unable. To form of the prime is XYYX such as 2^2007+2007^2.
> I have many PRP's to check with the smallest being around 10k digits.

It looks like you could be rehashing stuff that's already been done:

http://www.leyland.vispa.com/numth/primes/xyyx.htm

Are you aware of that web page?

A lot of PRPs there waiting for a proof...
• ... 2^2007+2007^2. ... digits. ... Turns out I was rehashing some stuff. Using the list, I ve verified some of the PRPs needing a proof. Also, I ve been
Message 4 of 4 , Dec 15, 2006
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--- In primenumbers@yahoogroups.com, "jbrennen" <jb@...> wrote:
>
> --- In primenumbers@yahoogroups.com, "Bryan" <beyastard@> wrote:
> >
> > How can one prove the primality of a PRP when every program I've
> > tried is unable. To form of the prime is XYYX such as
2^2007+2007^2.
> > I have many PRP's to check with the smallest being around 10k
digits.
>
> It looks like you could be rehashing stuff that's already been
done:
>
>
> http://www.leyland.vispa.com/numth/primes/xyyx.htm
>
> Are you aware of that web page?
>
> A lot of PRPs there waiting for a proof...
>
Turns out I was rehashing some stuff. Using the list, I've verified
some of the PRPs needing a proof. Also, I've been looking for
ar2220.zip everywhere but cannot find it. Been wanting to rewrite
VFYPR by Tony Forbes but lacking that file as it is no longer at his
website. I'm at a standstill as I don't know what the fuctions do,
don't know the structure of ireg, etc. Hopefully, someone out there
has this file and will upload it to the files section of this group.
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