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## Re: superpseudoprime

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• ... 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)
• 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
• 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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