- --- In primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> kannst Du zeigen dass

Oh dear, I am out of my linguistic depth:

> 2^(2^43112609 - 1) - 1

> ist keine Primzahl, oder dass

> (2^(2^43112609 - 1) + 1)/3

> ist keine Primzahl?

I forgot that Norman speaks backwards :-)

Correction:

> kannst Du zeigen dass

Translation:

> 2^(2^43112609 - 1) - 1

> keine Primzahl ist, oder dass

> (2^(2^43112609 - 1) + 1)/3

> keine Primzahl ist?

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

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.

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