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Re: [PrimeNumbers] More on complex primes

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  • 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 1 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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