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18689Re: the RH and predictability

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  • Werner D. Sand
    Feb 7, 2007
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      For example 2 adjacent gaps cannot be equal if they aren't multiple of
      6. For example the gap between 2 pairs of twins is at least 4. For
      example each prime number has the form 2n+/-1, 3n+/-1, 4n+/-1, 6n+/-1.
      Each pair of twins has the form 12n+-1, there are approximate formulas
      for the nth prime and the number of primes < x and so on. You cannot
      call all this random ore unpredictable. Of course the prime numbers are
      distributed as regularly as possible, that's a tautology. In
      mathematics everything is as regular as possible. Is pi random? Build
      P=2,357111317192329…, and you have the same case as pi. Consider the
      primes to be an irrational number, and there are no problems. If you
      mean there is no formula f(n) which produces primes for each n, then
      you are right. In this sense primes are random. (I am not quite sure –
      there is a formula p=[k^n^3] (H.W.Mills) which is said to produce only
      prime numbers). If you define "formula" as an algorithm, as a
      calculation instruction such as the sieve of Eratosthenes, then the
      primes are not random but simply what they are. Perhaps the compound
      numbers are random? Or are they only non-transparently complicated?

      Werner
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