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14093Re: Primes of the form (n^n-1)/(n-1)

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  • eharsh82
    Nov 29, 2003
      I have worked on these at the same time I worked on 2*a^a+-1. N must
      be prime in order for the above to be prime. I have searched for
      PRP's for a large n value (above 10000) and found only these 4.
      Probably the number of primes of this type are finite.
      As for n=13 and 19, both are prime.

      Harsh Aggarwal


      --- 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]
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