From: Lee Corbin (lcorbin@tsoft.com)
Date: Tue Jun 18 2002 - 10:40:34 MDT
Eliezer writes
> Lee Corbin wrote:
> >
> > If they think about 2^16 - 1, then they discover just
> > as we do that it's prime.
>
> That can't be right. (65536 - 1) ends in 5. A quick check shows that 65535
> == 3 * 5 * 17 * 257.
Oops. Thanks for the correction! I was trying to think of
a famous prime, and forgot that you have to *add* one to
2^2^4 to get Fermat's fifth prime (Fn = 3, 5, 17, 257, 65537...)
instead of *subtracting* one.
But you have just pointed out something VERY WEIRD! If you
take the 5th Fermat prime, 65537, and make my same mistake
in its calculation to get 65535, then *that* number factors
into a product consisting of ALL the previous Fermat primes!
I wonder what 3 * 5 * 17 * 257 * 65537 plus 2 is. (Perhaps
similar ratiocinations led Fermat to conjecture that all his
Fn were prime.) Or was that just a coincidence?
Lee
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