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14098Re: Primes of the form (n^n-1)/(n-1)

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  • tdn1952
    Nov 30, 2003
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      --- In primenumbers@yahoogroups.com, "julienbenney" <jpbenney@f...>
      wrote:
      > Moving away from prime quadruples, there is another topic that I
      have
      > never seen anything written about that I am curious about.
      >
      > I know from tables of generalised repunit primes that
      ((n^n)-1)/(n-1)
      > is prime for n = 2, 3, 19 and 31 and for no other n up to 1,000. Is
      > there a theorem that could show these four numbers to be the only n
      for
      > which ((n^n)-1)/(n-1) is prime?
      >
      > Also, when was the primality of 19^19-1/18 and 31^31-1/30 proved?
      [I am
      > curious]


      The next value of n that yields a probable prime is 7547. See
      sequence A088790 has more information.

      Tony
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