## More on complex primes

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• Thank you. I ve learned that there are complex primes, that they differ from the real primes, and that they seem to be symmetrically arrayed in the complex
Message 1 of 2 , Mar 20, 2007
Thank you.

I've learned that there are complex primes, that they differ from the real primes,
and that they
seem to be symmetrically arrayed in the complex plane. In looking at the Java
applet (which
shows this symmetrical distribution), it looked very much like a CA, and I
wonder, given that
distribution (the way it looks on a grid), if it is possible to treat it as if
it were a CA and to
deduce the CA rule needed to generate it.
• ... CA can be computationally complete, so it is possible to get CA to generate all such primes (or maybe perhaps only irreducibles) in any ring. The CA sieve
Message 2 of 2 , Mar 20, 2007
--- terranorca <terranorca@...> wrote:
> I've learned that there are complex primes, that they differ from the real
> primes,
> and that they
> seem to be symmetrically arrayed in the complex plane. In looking at the Java
> applet (which
> shows this symmetrical distribution), it looked very much like a CA, and I
> wonder, given that
> distribution (the way it looks on a grid), if it is possible to treat it as
> if it were a CA and to
> deduce the CA rule needed to generate it.

CA can be computationally complete, so it is possible to get CA to generate all
such primes (or maybe perhaps only irreducibles) in any ring. The CA sieve of
eratosthenes is a wonderful sight to behold. I cannot imagine why a
multidimensional CA couldn't perform the same task for Gaussian or
Eisensteinian primes.

Phil

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