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Forward: Mihailescu's CIDE

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  • Chris Caldwell
    From: Jens Franke (Tuesday, December 11, 2012 4:58 AM) We have confirmed the primality of the Leyland numbers 3110^63+63^3110 (5596 digits) and
    Message 1 of 6 , Dec 11, 2012
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      From: Jens Franke (Tuesday, December 11, 2012 4:58 AM)

      We have confirmed the primality of the Leyland numbers 3110^63+63^3110
      (5596 digits) and 8656^2929+2929^8656 (30008 digits) by an implementation of a version of Mihailescu's CIDE. The certificates may be found at

      http://www.math.uni-bonn.de:people/franke/ptest/x3110y63.cert.tar.bz2

      and

      http://www.math.uni-bonn.de:people/franke/ptest/x8656y2929.cert.tar.bz2 ,

      a description of their format together with proofs of the underlying mathematical statements is at

      http://www.math.uni-bonn.de:people/franke/ptest/fmt-0.1.pdf .

      Tables of powers of Gauss sums used by the certificates are at

      http://www.math.uni-bonn.de:people/franke/Gspk.tar.bz2 .

      Calculations were carried out using resources at the Hausdorff Center for Mathematics (http://www.hausdorff-center.uni-bonn.de), the Institute for Numerical Simulation (http://www.ins.uni-bonn.de/institut/), and LACAL (http://lacal.epfl.ch )

      J. Franke, T. Kleinjung, A. Decker, J. Ecknig, A. Großwendt
    • paulunderwooduk
      ... I have emailed Henri Lifchitz about Anatoly F. Selevich s ex-PRP:
      Message 2 of 6 , Dec 11, 2012
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        --- In primenumbers@yahoogroups.com, Chris Caldwell <caldwell@...> wrote:
        >
        > From: Jens Franke (Tuesday, December 11, 2012 4:58 AM)
        >
        > We have confirmed the primality of the Leyland numbers 3110^63+63^3110
        > (5596 digits) and 8656^2929+2929^8656 (30008 digits) by an implementation of a version of Mihailescu's CIDE. The certificates may be found at
        >
        > http://www.math.uni-bonn.de:people/franke/ptest/x3110y63.cert.tar.bz2
        >
        > and
        >
        > http://www.math.uni-bonn.de:people/franke/ptest/x8656y2929.cert.tar.bz2 ,
        >
        > a description of their format together with proofs of the underlying mathematical statements is at
        >
        > http://www.math.uni-bonn.de:people/franke/ptest/fmt-0.1.pdf .
        >
        > Tables of powers of Gauss sums used by the certificates are at
        >
        > http://www.math.uni-bonn.de:people/franke/Gspk.tar.bz2 .
        >
        > Calculations were carried out using resources at the Hausdorff Center for Mathematics (http://www.hausdorff-center.uni-bonn.de), the Institute for Numerical Simulation (http://www.ins.uni-bonn.de/institut/), and LACAL (http://lacal.epfl.ch )
        >
        > J. Franke, T. Kleinjung, A. Decker, J. Ecknig, A. Großwendt
        >

        I have emailed Henri Lifchitz about Anatoly F. Selevich's ex-PRP:
        http://www.primenumbers.net/prptop/searchform.php?form=8656^2929%2B2929^8656&action=Search

        Paul
      • djbroadhurst
        ... Here is Preda s method for cyclotomic numbers: http://arxiv.org/pdf/0709.4113v1.pdf David
        Message 3 of 6 , Dec 11, 2012
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          > From: Jens Franke (Tuesday, December 11, 2012 4:58 AM)
          > We have confirmed the primality of the Leyland numbers
          > 3110^63+63^3110 (5596 digits) and
          > 8656^2929+2929^8656 (30008 digits)
          > by an implementation of a version of Mihailescu's CIDE.

          Here is Preda's method for cyclotomic numbers:
          http://arxiv.org/pdf/0709.4113v1.pdf

          David
        • thefatphil
          ... How does that relate to: Dual Elliptic Primes and Cyclotomy Primality Proving Preda Mihailescu and Francois Morain Which I downloaded as
          Message 4 of 6 , Dec 12, 2012
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            --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
            > > From: Jens Franke (Tuesday, December 11, 2012 4:58 AM)
            > > We have confirmed the primality of the Leyland numbers
            > > 3110^63+63^3110 (5596 digits) and
            > > 8656^2929+2929^8656 (30008 digits)
            > > by an implementation of a version of Mihailescu's CIDE.
            >
            > Here is Preda's method for cyclotomic numbers:
            > http://arxiv.org/pdf/0709.4113v1.pdf

            How does that relate to:
            """
            Dual Elliptic Primes and Cyclotomy Primality Proving
            Preda Mihailescu and Francois Morain
            """
            Which I downloaded as 10.1.1.29.6756.pdf from goodness-knows-where only an hour ago (my stack too full, as soon as something's popped, it's purged).

            Phil (pop!)
          • djbroadhurst
            ... That 1999 conference report may be obtained from http://130.203.133.150/viewdoc/download?doi=10.1.1.29.6756&rep=rep1&type=pdf As Phil has noted, the
            Message 5 of 6 , Dec 12, 2012
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              --- In primenumbers@yahoogroups.com,
              "thefatphil" <thefatphil@...> wrote:

              > > Here is Preda's method for cyclotomic numbers:
              > > http://arxiv.org/pdf/0709.4113v1.pdf
              >
              > How does that relate to:
              > Dual Elliptic Primes and Cyclotomy Primality Proving
              > Preda Mihailescu and Francois Morain
              > Which I downloaded as 10.1.1.29.6756.pdf from goodness-knows-where

              That 1999 conference report may be obtained from

              http://130.203.133.150/viewdoc/download?doi=10.1.1.29.6756&rep=rep1&type=pdf

              As Phil has noted, the single-author paper of 2007
              makes no reference to it, which seems a little odd.

              David
            • Phil Carmody
              ... Thanks to my NMBRTHRY posting, I ve ended up in a delightful off-list chat with Preda himself, in which he has leaked the info that his CycloProv did
              Message 6 of 6 , Dec 14, 2012
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                --- On Wed, 12/12/12, djbroadhurst wrote:
                > --- In primenumbers@yahoogroups.com "thefatphil" <thefatphil@...> wrote:
                > > > Here is Preda's method for cyclotomic numbers:
                > > > http://arxiv.org/pdf/0709.4113v1.pdf
                > >
                > > How does that relate to:
                > > Dual Elliptic Primes and Cyclotomy Primality Proving
                > > Preda Mihailescu and Francois Morain
                > > Which I downloaded as 10.1.1.29.6756.pdf from goodness-knows-where
                >
                > That 1999 conference report may be obtained from
                >
                > http://130.203.133.150/viewdoc/download?doi=10.1.1.29.6756&rep=rep1&type=pdf
                >
                > As Phil has noted, the single-author paper of 2007
                > makes no reference to it, which seems a little odd.

                Thanks to my NMBRTHRY posting, I've ended up in a delightful off-list chat with Preda himself, in which he has leaked the info that his CycloProv did indeed have the earliest seeds of CIDE within it, amongst other little nuggets.

                There's definitely an interesting future for this algorithm...

                Phil
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