Loading ...
Sorry, an error occurred while loading the content.
 

fermat pseudoprimes p=n^2+n+1

Expand Messages
  • bhelmes_1
    A beautifull day Do you know whether there exists a fermat pseudoprime of the form p:=n^2+n+1 By the way i started a small collection of 1000 digit primes of
    Message 1 of 3 , Jul 10, 2010
      A beautifull day

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

      By the way i started a small collection of 1000 digit primes of this form, only for your pleasure :-)

      http://beablue.selfip.net/devalco/Collection/

      There are approximately 2000 definitiv primes checked by pfgw in the database

      Nice greetings from the primes
      Bernhard
    • 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 2 of 3 , Jul 10, 2010
        --- 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 3 of 3 , Jul 10, 2010
          --- 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
        Your message has been successfully submitted and would be delivered to recipients shortly.