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RE: we are now 1087...

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  • Douglas Chester
    Can t think of anything off the top of my head, and David Wells s Curious and Interesting Numbers does not have an entry. According to Chris Caldwell s Prime
    Message 1 of 3 , Jul 13 2:25 PM
      Can't think of anything off the top of my head, and David
      Wells's "Curious and Interesting Numbers" does not have an entry.
      According to Chris Caldwell's Prime Curios

      1087 is a prime factor of the 32nd Lucas number (the first such
      number with index of form 2^n that is composite).
      The largest known number such that (10000^n+1)/10001 is probably
      prime.


      Perhaps we should try and find another half a dozen new members, then
      we are 1093. Wells's entry for 1093 is a bit more interesting:

      "2^1092 - 1 is divisible by 1093. Only one other number is known
      below 4 * 10^12 with this property, 3511.
      In 1909 Wieferich created a sensation by proving that if Fermat's
      equation, x^p + y^p = z^p, has a solution in whih p is an odd prime
      that does notr divide any of x, y or z, then 2^(p-1) - 1 is divisible
      by p^2. As facts about Fermat's last theorem go, this is remarkably
      simple. That 1093 and 3511 are the only solutions below 4 * 10^12
      means that only these two cases of Fermat's theorem need to be
      considered, below that limit, of p does not divide xyz."

      Douglas Chester







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