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Re: Primes from permutation of prime digits

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  • Mark Underwood
    ... Interesting. It s surprising to me that the number of odd digits barely outnumbers the number of even digits in these primes with maximum perms. Must be a
    Message 1 of 7 , Feb 13, 2009
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      --- In primenumbers@yahoogroups.com, zak seidov <zakseidov@...> wrote:

      > > > We have the next table of
      > > > minimal primes p with given perm:
      > > > {perm,p)
      > > > {1,2}
      > > > {10,1097}
      > > > {100,1006991}
      > > > {1000,12338449}
      ...
      > > zak(12338449)
      > > = 4000
      > > Using your definition & my code the first with
      > > perm>10^4 I found
      > > (without exhaustive search) is:
      > > 11111117 15120
      ...
      > first case of perm(p)>10^4 is perm(100123697)=10042
      > and of course i mean "distinct primes",
      > otherwise perm(11)=2 - curious enough.
      > maximal perm for first 2*10^7 primes is
      > perm(102345697)=30852 (distinct primes!)
      > zak
      >



      Interesting. It's surprising to me that the number of odd digits
      barely outnumbers the number of even digits in these primes with
      maximum perms. Must be a good reason ...

      Mark
    • Mark Underwood
      ... Scrap that. It s not that surprising to me anymore. :) Mark
      Message 2 of 7 , Feb 13, 2009
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        --- In primenumbers@yahoogroups.com, "Mark Underwood"
        <mark.underwood@...> wrote:
        >

        > Interesting. It's surprising to me that the number of odd digits
        > barely outnumbers the number of even digits in these primes with
        > maximum perms. Must be a good reason ...
        >

        Scrap that. It's not that surprising to me anymore. :)

        Mark
      • David Broadhurst
        I prefer zak(1123465789) = 152526 to zak(1023345679) = 156227 since the former does not invoke leading zeros. David
        Message 3 of 7 , Feb 14, 2009
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          I prefer
          zak(1123465789) = 152526 to
          zak(1023345679) = 156227 since
          the former does not invoke leading zeros.

          David
        • David Broadhurst
          ... Thereafter, 11-digit primes become somewhat memory-intensive, in my simple-minded implementation, using GP s vecsort . Might Zak and/or Maximilian confirm
          Message 4 of 7 , Feb 14, 2009
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            --- In primenumbers@yahoogroups.com, "David Broadhurst"
            <d.broadhurst@...> wrote:

            > I prefer
            > zak(1123465789) = 152526 to
            > zak(1023345679) = 156227 since
            > the former does not invoke leading zeros.

            Thereafter, 11-digit primes become somewhat memory-intensive,
            in my simple-minded implementation, using GP's "vecsort".

            Might Zak and/or Maximilian confirm that
            zak(10123457689) = 1404250
            without duplication of primes, but allowing Zak's leading zeros ?

            David
          • Maximilian Hasler
            ... yes: zak(10123457689) %1 = 2808500 2808500/2 (symmetry factor for exchange of the two 1 s) %2 = 1404250 Maximilian
            Message 5 of 7 , Feb 15, 2009
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              > Thereafter, 11-digit primes become somewhat memory-intensive,
              > in my simple-minded implementation, using GP's "vecsort".
              >
              > Might Zak and/or Maximilian confirm that
              > zak(10123457689) = 1404250
              > without duplication of primes, but allowing Zak's leading zeros ?

              yes:
              zak(10123457689)
              %1 = 2808500
              2808500/2 \\ (symmetry factor for exchange of the two 1's)
              %2 = 1404250

              Maximilian
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