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From: rdsilverman@qed.com
Subject: Re: 9, prime gone bad. was RE: zero blah blah
Message-ID: <297cc$a224.39a@www.qed.com>
Date: Fri, 09 Feb 96 10:11:31 PDT
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In article <4fdvcs$s9e@status.gen.nz>, <ericf@central.co.nz> writes:
> 
> rusin@washington.math.niu.edu (Dave Rusin) wrote:
> >This is false. There are methods of determining the primality of an
> >integer which are much faster and which, in particular, do not imply
> >any knowledge of the factors if the number is indeed shown to be
> >composite. Just to give a simple and useful example, if  2^n (mod n)
> >isn't  2, then  n  isn't prime.
> 
> All you have demonstrated is that the determination can be done
> quickly for SOME numbers, i.e. those which can be quickly falsified.
> You have not demonstrated that prime numbers can be quickly verified
> as being prime.
> 
Sigh.

Both the Elliptic Curve Primality test and the Cyclotomic Ring test
(aka Cohen-Lenstra) are prime proving algorithms which do not depend
upon trial division.

I wish people who have not studied a subject would stop making such
sweeping pronouncements. (i.e. that there are no algorithms to prove
primality).


Note also that I have ignored Wilson's Theorem as well!


