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Re: superpseudoprime

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  • djbroadhurst
    ... Oh dear, I am out of my linguistic depth: I forgot that Norman speaks backwards :-) ... Translation: Can you show that 2^(2^43112609 - 1) - 1 is not prime,
    Message 1 of 22 , Sep 30, 2009
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      --- In primenumbers@yahoogroups.com,
      "djbroadhurst" <d.broadhurst@...> wrote:

      > kannst Du zeigen dass
      > 2^(2^43112609 - 1) - 1
      > ist keine Primzahl, oder dass
      > (2^(2^43112609 - 1) + 1)/3
      > ist keine Primzahl?

      Oh dear, I am out of my linguistic depth:
      I forgot that Norman speaks backwards :-)

      Correction:

      > kannst Du zeigen dass
      > 2^(2^43112609 - 1) - 1
      > keine Primzahl ist, oder dass
      > (2^(2^43112609 - 1) + 1)/3
      > keine Primzahl ist?

      Translation:

      Can you show that
      2^(2^43112609 - 1) - 1
      is not prime, or that
      (2^(2^43112609 - 1) + 1)/3
      is not prime?

      If (like me) you cannot, then you also
      cannot show that the proven Super Poulet
      4^(2^43112609 - 1) - 1)/3
      is also a super-pseudoprime,
      according to the strict definition of Maximilian.

      David (relieved to return to English)
    • djbroadhurst
      86225219*5259738299*5949540043*12482997260297*(2^43112609-1) is the largest known completely factorized superpseudoprime, discovered by Edson Smith
      Message 2 of 22 , Oct 1, 2009
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        86225219*5259738299*5949540043*12482997260297*(2^43112609-1)
        is the largest known completely factorized superpseudoprime,
        discovered by Edson Smith
        http://primes.utm.edu/bios/page.php?id=1498
        and Alex Kruppa
        http://www.mersenneforum.org/showpost.php?p=142690&postcount=712

        Puzzle: Find another superpseudoprime with at least
        a million decimal digits and precisely 32 divisors.

        Hint: This may be done by judicious googling.

        David Broadhurst
      • djbroadhurst
        A base-b superpseudoprime is a non-semiprime composite number all of whose composite divisors are base-b pseudoprimes.
        Message 3 of 22 , Oct 2, 2009
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          A base-b superpseudoprime is a non-semiprime composite
          number all of whose composite divisors are base-b pseudoprimes.

          1340753*2011129*803278043*(89^11971-1)/88 is a gigantic
          base-89 superpseudoprime with precisely 11 composite divisors.

          Puzzle 89: For a base with 89 > b > 2, find a gigantic
          base-b superpseudoprime with precisely 26 composite divisors.

          Hint: For the meat, see http://aruljohn.com/Bible/kjv/luke/12/42

          David Broadhurst
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