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Number 19

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  • Ali Adams
    Is this an expected property of the number 19 or even 9? 19 digits 9191919191919191919 = 3 * 3 * 1021324354657687991 which has the digits n n-1 n+1 repeating
    Message 1 of 5 , Sep 9, 2010
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      Is this an expected property of the number 19 or even 9?

      19 digits 9191919191919191919 = 3 * 3 * 1021324354657687991

      which has the digits n n-1 n+1 repeating as follows:

      = 9 * (n n-1 n+1 (n+1) (n+1)-1 (n+1)+1 ...) / 10

      Also note:
      23 digits 91919191919191919191919 is prime

      17 digits 91919191919191919 is prime.

      11 digits 91919191919 is prime.

      9 digits 919191919 is prime.

      3 digits 919 is prime.

      Ali
      Prime numbers are God's signature!
      www.heliwave.com






      [Non-text portions of this message have been removed]
    • djbroadhurst
      ... The next probable prime has 25229 digits: (91*10^25229-19)/99 is Fermat and Lucas PRP! (166.8607s+0.0024s) David
      Message 2 of 5 , Sep 10, 2010
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        --- In primenumbers@yahoogroups.com, Ali Adams
        <alipoland@...> wrote:

        > 23 digits 91919191919191919191919 is prime

        The next probable prime has 25229 digits:

        (91*10^25229-19)/99 is Fermat and Lucas PRP! (166.8607s+0.0024s)

        David
      • Lélio Ribeiro de Paula
        ... and was found by Patrick de Geest in july 2004: http://www.primenumbers.net/prptop/searchform.php?form=%3F%2F99 Lélio [Non-text portions of this message
        Message 3 of 5 , Sep 10, 2010
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          >
          > --- In primenumbers@yahoogroups.com, David Broadhurst wrote:
          >
          > > 23 digits 91919191919191919191919 is prime
          >
          > The next probable prime has 25229 digits:
          >
          > (91*10^25229-19)/99 is Fermat and Lucas PRP! (166.8607s+0.0024s)
          >
          > David
          >
          >
          >

          and was found by Patrick de Geest in july 2004:

          http://www.primenumbers.net/prptop/searchform.php?form=%3F%2F99


          Lélio


          [Non-text portions of this message have been removed]
        • Makoto Kamada
          ... According to Patrick de Geest s website, Hans Rosenthal found it. http://www.worldofnumbers.com/undulat.htm#supp919 Factorizations of (91*10^(2n+1)-19)/99
          Message 4 of 5 , Sep 10, 2010
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            On 2010/09/10 21:20, Lélio Ribeiro de Paula wrote:
            >> --- In primenumbers@yahoogroups.com, David Broadhurst wrote:
            >>
            >> The next probable prime has 25229 digits:
            >>
            >> (91*10^25229-19)/99 is Fermat and Lucas PRP! (166.8607s+0.0024s)
            >
            > and was found by Patrick de Geest in july 2004:
            >
            > http://www.primenumbers.net/prptop/searchform.php?form=%3F%2F99

            According to Patrick de Geest's website, Hans Rosenthal found it.
            http://www.worldofnumbers.com/undulat.htm#supp919

            Factorizations of (91*10^(2n+1)-19)/99 are here:
            http://www.asahi-net.or.jp/~kc2h-msm/mathland/aba/aba919.htm

            Makoto Kamada
          • maximilian_hasler
            ... The 15 digit number 151515151515151 is prime, too ; and it is the only such prime (undulating : aba...ba with ab = 10*a+b or ba = 10*b+a digits. M.
            Message 5 of 5 , Sep 10, 2010
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              > 23 digits 91919191919191919191919 is prime
              > 17 digits 91919191919191919 is prime.
              > 11 digits 91919191919 is prime.
              > 9 digits 919191919 is prime.

              The 15 digit number 151515151515151 is prime, too ;
              and it is the only such prime (undulating : aba...ba
              with ab = 10*a+b or ba = 10*b+a digits.

              M.
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