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superpseudoprime puzzle

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  • djbroadhurst
    86225219*5259738299*5949540043*12482997260297*(2^43112609-1) is the largest known completely factorized superpseudoprime, discovered by Edson Smith
    Message 1 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 2 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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