Fwd: Re: Yet another Lucas-Lehmer like primality test ?
- Forwarding to list:
--- Mike Oakes <mikeoakes2@...> wrote:
> --- In firstname.lastname@example.org, "j_chrtn" <j_chrtn@...> wrote:() ASCII ribbon campaign () Hopeless ribbon campaign
> > --- In email@example.com, Phil Carmody <thefatphil@>
> > wrote:
> > >
> > > Aside - who is recording these primes, I don't think it's one of
> > Jens' or
> > > Steven's forms, is it?
> > I don't know if someone officially records this form of primes. I
> > just know that we (Mike Oakes, Predrag Minovic, myself and maybe
> > other people) have recorded many PRP of this form to Henri Lifchitz
> > probable primes page.
> > The largest known PRP of this form (which is my current record) is
> > 10^282493-9^282493.
> > J-L.
> [strange coincidence]
> I'm right now within a day or so of completing a multi-year project
> to find all PRPs of this form, viz. b^p-(b-1)^p, for 3 <= b <= 1000,
> p < 10000, with primality proofs for all p < 1000.
> There's just one more PRIMO certification (c. 9000 bits) to do, then
> I'll post the results on a web page.
> -Mike Oakes
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- --- In firstname.lastname@example.org, Phil Carmody <thefatphil@...>
> >Yes Phil, I knew Mike was looking all PRP numbers of this form for b up
> > [strange coincidence]
> > I'm right now within a day or so of completing a multi-year project
> > to find all PRPs of this form, viz. b^p-(b-1)^p, for 3 <= b <= 1000,
> > p < 10000, with primality proofs for all p < 1000.
> > There's just one more PRIMO certification (c. 9000 bits) to do, then
> > I'll post the results on a web page.
> > -Mike Oakes
to 1000 and p up to 10000. But I didn't know that he had almost
terminated this work and that he also had in fact certified all these
PRP with primo.
Great job !
It would be interesting to have a table of all these primes. I would
like to check whether my statements are compatible with Mike's result
BTW, Mike : does this titanic work reveals some interesting (non
trivial) properties for this form of numbers ?