Loading ...
Sorry, an error occurred while loading the content.
 

Fwd: Re: Yet another Lucas-Lehmer like primality test ?

Expand Messages
  • Phil Carmody
    ... () ASCII ribbon campaign () Hopeless ribbon campaign / against HTML mail / against gratuitous bloodshed [stolen with permission from
    Message 1 of 2 , May 6, 2007
      Forwarding to list:

      --- Mike Oakes <mikeoakes2@...> wrote:
      > --- In primenumbers@yahoogroups.com, "j_chrtn" <j_chrtn@...> wrote:
      > >
      > > --- In primenumbers@yahoogroups.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


      () ASCII ribbon campaign () Hopeless ribbon campaign
      /\ against HTML mail /\ against gratuitous bloodshed

      [stolen with permission from Daniel B. Cristofani]

      __________________________________________________
      Do You Yahoo!?
      Tired of spam? Yahoo! Mail has the best spam protection around
      http://mail.yahoo.com
    • j_chrtn
      ... Yes Phil, I knew Mike was looking all PRP numbers of this form for b up to 1000 and p up to 10000. But I didn t know that he had almost terminated this
      Message 2 of 2 , May 9, 2007
        --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...>
        wrote:
        > >
        > > [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
        >

        Yes Phil, I knew Mike was looking all PRP numbers of this form for b up
        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
        or not.

        BTW, Mike : does this titanic work reveals some interesting (non
        trivial) properties for this form of numbers ?

        Best regards,

        J-L.
      Your message has been successfully submitted and would be delivered to recipients shortly.