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

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  • Joshua Zucker
    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
    Message 1 of 3 , Jun 2, 2007
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      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
    • 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 2 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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