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Re: fermat pseudoprimes p=n^2+n+1

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  • djbroadhurst
    ... Yes. These [n, p] pairs make p = n^2 + n + 1 a Carmichael number: [2304, 5310721] [47735, 2278677961] [97944, 9593125081] [172799, 29859667201] [683808255,
    Message 1 of 3 , Jul 10 4:38 PM
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      --- In primenumbers@yahoogroups.com,
      "bhelmes_1" <bhelmes@...> wrote:

      > Do you know whether there exists a fermat pseudoprime of the form
      > p:=n^2+n+1

      Yes. These [n, p] pairs make
      p = n^2 + n + 1
      a Carmichael number:

      [2304, 5310721]
      [47735, 2278677961]
      [97944, 9593125081]
      [172799, 29859667201]
      [683808255, 467593730289953281]

      David
    • djbroadhurst
      ... The largest has 208601 digits and was found by PrimeMogul himself: http://primes.utm.edu/primes/page.php?id=83711 David
      Message 2 of 3 , Jul 10 5:59 PM
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        --- In primenumbers@yahoogroups.com,
        "bhelmes_1" <bhelmes@...> wrote:

        > p:=n^2+n+1
        ...
        > i started a small collection of 1000 digit primes of this form

        The Prime Pages list 1357 primes of this form:

        > Used 1.2427 second(s) to find
        > 1357 primes matching the selection criteria:
        > Description must match: Phi\\(3,.*\\)$.

        The largest has 208601 digits and was found by PrimeMogul himself:
        http://primes.utm.edu/primes/page.php?id=83711

        David
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