## superpseudoprime puzzle

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• 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
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.

• 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
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