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Are prime fractals, or have a fractal geometry ?

  1. are prime fractals, or have a fractal geometry ??

    my idea is, if we consider the geometry of primes could we conclude they form a fractal ? , for example if we represent all the primes using a computer, it will give us a fractal pattern.

    according to a paper http://arxiv.org/PS_cache/chao-dyn/pdf/9406/9406003v1.pdf

    zeta function (which is just a product of primes for s >1) could be a fractal, but how about primes ?¿?
     
  2. jcsd
  3. CRGreathouse

    CRGreathouse 3,682
    Science Advisor
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    Re: are prime fractals, or have a fractal geometry ??

    In what sense are you saying the primes are (or may be) fractals? Are they self-similar? Do they have non-integer dimension?
     
  4. Re: are prime fractals, or have a fractal geometry ??

    my question is, if we use the Sieve of Eratosthenes.. for big scales (let us say 1000000000000000000000000 primes or similar) then the picture drawn is a fractal, for example.
     
  5. Re: are prime fractals, or have a fractal geometry ??

    If I interpret your question correctly: no, they don't, because of the prime number theorem.
     
  6. Re: are prime fractals, or have a fractal geometry ??

    This is an amazing question, was thinking about it last night. PGP and Gnupg both use prime numbers to generate the keys. If the Mandelbrot fractal pattern that Mandelbrot saw in the noise in the network lines is the same as the fractal's chaotic patterns we see then hummmmmmmmm....this is a good very good question, did you get an answer yet?
     
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