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More on complex primes

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  • terranorca
    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
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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 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.
    • Phil Carmody
      ... 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
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        --- 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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