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Re: [PrimeNumbers] Another question from a non-mathematician

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  • Shi Huang
    Mathematics is linked with determinism and predictability. Thus the seeming randomness of primes is striking. The duality is what makes the primes so
    Message 1 of 3 , Jun 4, 2007
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      Mathematics is linked with determinism and
      predictability. Thus the seeming randomness of primes
      is striking. The duality is what makes the primes so
      mysterious and interesting. If you google 'duality
      prime numbers', you will find this paper
      (www.secamlocal.ex.ac.uk/
      people/staff/mrwatkin/isoc/huang.pdf)
      that provides an elementary proof for the duality of
      primes.

      --- Joshua Zucker <joshua.zucker@...> wrote:

      > I think the randomness and bell curve are in one
      > sense much more
      > predictable than primes:
      > if you flip a coin long enough, you are eventually
      > going to get N
      > heads in a row for sure.
      >
      > But with primes, we don't know whether or not in the
      > long run you will
      > get infinitely many
      > twin primes or not.
      >
      > The problem is, really random things will actually
      > do everything in
      > the long run. But the primes aren't random!
      >
      > That is, the bell curve describes what random
      > variables tend to do in
      > the long run (namely, be off the mean by about
      > sqrt(n)).
      >
      > But while the prime number theorem is similar for
      > primes, since the
      > primes ARE predictable we need to understand a lot
      > more about how they
      > deviate in the short run from their long run
      > average.
      >
      > --Joshua ZUcker
      >




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