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Re: [PrimeNumbers] Re: proving the Riemann hypothesis

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  • Shi Huang
    ... If it remains unknown whether primes can be predicted, then at least one side of the duality is unproven. If one day, someone finds a formula to predict
    Message 1 of 40 , Feb 2, 2007
      > To the extent that I can understand what you're
      > saying, I
      > think that the "yin yang duality" of primes is
      > already proven.
      >

      If it remains unknown whether primes can be predicted,
      then at least one side of the duality is unproven. If
      one day, someone finds a formula to predict individual
      prime, then there will be no duality and primes would
      cease to be interesting. So to prove the duality, one
      must first prove that primes cannot be predicted. I
      think I may have a prove of this.

      Proving the RH will prove that primes are bound by
      laws but will have no effect on the issue of
      predictability. So it will not prove the yin yang
      duality. In fact, I dont know any single conjecture
      that, if proven, can prove the yin yang duality of
      primes. So to prove the duality is a more fundamental
      problem than the RH. One does not even know how to go
      about it, which explains why no conjecture on this has
      been proposed. My conjecture of a prime generating
      law that demands both unpredicatability and lawfulness
      is one way of doing it. Finding such a law would
      prove the duality. If the duality is proven, its
      deductions must be true, which would include what the
      RH essentially says in layman terms.



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    • Werner D. Sand
      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
      Message 40 of 40 , Feb 7, 2007
        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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