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Perry numbers - formerly known as "Wilde Primes"

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  • richard_heylen
    Hey guys! I ve recently done some more work on so-called Wilde Primes although I suggest that if we keep any of Jon Perry s name we should call them Perry
    Message 1 of 2 , Feb 5, 2004
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      Hey guys! I've recently done some more work on so-called "Wilde
      Primes" although I suggest that if we keep any of Jon Perry's name we
      should call them "Perry numbers" by analogy with Riesel and
      Sierpinski numbers.

      http://www.users.globalnet.co.uk/~perry/maths/wildeprimes/wildeprimes.
      htm

      Under my proposed naming scheme, a Perry number k is never prime no
      matter how many 1s you add to the right hand side of its base-10
      representation. Primes thus obtained would be Perry primes. Although
      the default base would be 10, Perry numbers and Perry primes exist in
      other bases although perhaps the non base-10 cases could be subsumed
      under a generalization of Riesel and Sierpinski numbers. We could
      therefore alternatively describe Perry numbers as base-10 Riesel
      numbers.

      We are therefore looking for numbers k for which ((9k+1)*10^n-1)/9 is
      never prime. Jack Brennen conjectured that 176 is the lowest Perry as
      it has a covering set using the primes 3, 7, 11 and 13. Four lower
      candidates existed but eventually fairly large Perry probable primes
      were found for three of these values. One of these probable primes
      was confirmed as prime using Primo. Another should be provable using
      current methods but the third will be impossible using general
      primality proving software. Perhaps Proth's theorem can be extended
      to bases other than 2? ;-)

      I am pleased to announce, however, that Jack Brennen's conjecture is
      false as I have proved that 38 is the smallest Perry number. It's
      quite interesting to see why. I commend this problem to you as one
      where the aesthetics of the result are disproportionately high given
      the ease of the solution.

      Richard Heylen
    • Jack Brennen
      ... Clear as day, now that it s been pointed out. After all, who could possibly miss the fact that 38 equals (7^3-1)/9... Good one! Jack
      Message 2 of 2 , Feb 5, 2004
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        > I am pleased to announce, however, that Jack Brennen's conjecture is
        > false as I have proved that 38 is the smallest Perry number.

        Clear as day, now that it's been pointed out.

        After all, who could possibly miss the fact that 38 equals (7^3-1)/9...

        Good one!

        Jack
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