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Re: adjacents and primes

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  • Mark Underwood
    Jens I don t know how you can go up that high, good lord! Amazing. Thank you for finding (at over 55,000 digits!) what I could never have hoped to. kind
    Message 1 of 6 , Jan 3, 2006
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      Jens I don't know how you can go up that high, good lord! Amazing.
      Thank you for finding (at over 55,000 digits!) what I could never
      have hoped to.

      kind regards,
      Mark




      --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
      <jens.k.a@g...> wrote:
      >
      (snip)

      > The smallest a>1 for which a^r + b^s is never prime for
      > b = a+/-1, s = r+/-1, and r,s <= a, is a = 13361.
      > This assumes prp's for smaller a are really primes.
      >
      > The cases where prp's above 3000 digits were needed:
      > 1252^1155 + 1253^1154 (3578 digits)
      > 3319^992 + 3318^991 (3493 digits)
      > 9818^765 + 9819^764 (3054 digits)
      > 9819^764 + 9818^765 (3054 digits, same prp as for a=9818)
      > 10127^888 + 10126^887 (3557 digits)
      > 11051^1176 + 11050^1177 (4760 digits)
      >
      > PrimeForm/GW made prp tests. 13361^13361 has 55126 digits.
      > I stopped there but guess there are primes for larger exponents.
      >
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