From: Dan McGuirk <mcguirk@enuxsa.eas.asu.edu>
Date: Tue, 12 Apr 94 21:58:50 PDT
To: cypherpunks@toad.com
Subject: Re: Prime Numbers
In-Reply-To: <9404120224.AA07676@toad.com>
Message-ID: <199404130501.WAA09532@enuxsa.eas.asu.edu>
MIME-Version: 1.0
Content-Type: text


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Eli Brandt writes:
> >    primes numbers who happen to be of the form (2^(2^n))+1 are called 
> >    Fermat primes. Some pretty large ones are known (could send a list...)

> Please do.  My recollection was that none existed above 65537.

Well, according to "An Introduction to the Theory of Numbers" by G.H.
Hardy and E.M. Wright you're correct.  They say the largest n for which
the Fermat prime F_n has been found is F_4 = 2^(2^4)+1 = 65537.  Of
course, this book was written in 1938 so the situation could have
changed since then.

F_n is known to be composite for
	7<=n<=16, n=18, 19, 21, 23, 36, 38, 39, 55, 63, 73
and others.  Not a very successful conjecture for Fermat, I suppose...

- -- 
Dan McGuirk						  djm@asu.edu
 When cryptography is outlawed, pkog ofklsjr vija fhsl ciehgoabykze.

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