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Re: [PrimeNumbers] Re: proving the Riemann hypothesis

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  • Shi Huang
    ... Dick, I am not a math specialist. So I was discouraged by earilier replies to my post, which implies what I have conjectured is similar to Bertrand s
    Message 1 of 40 , Feb 2, 2007
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      --- Dick <richard042@...> wrote:


      >
      > > I can prove that the gap must be smaller
      > > than P1xP1-P1. If P1 is 5, this means that the gap
      > > between 5 and its next prime must be smaller than
      > 5 x
      > > 5 -5=20.
      >
      > Much stronger than Bertrand's postulate and a very
      > sensible conjecture
      > heuristically.

      Dick,

      I am not a math specialist. So I was discouraged by
      earilier replies to my post, which implies what I have
      conjectured is similar to Bertrand's postulate. Could
      you please explain why you think it is much stronger?
      This may help me decide whether it is worthwhile to
      bother with a publication of the proof.

      I now also realized that my conjecture is not enough
      to prove the RH. It mearly says that the gap is not
      completely random but it does not say that the gap is
      as non-random as possble which is what the RH means.

      I wonder if you guys would consider the following a
      way of proving the RH:

      1. prove that primes are unpredictable, which thus
      gives its random flavor.

      2. prove that primes are generated by a precise law,
      where no randomness is involved. The only thing that
      would cause the law to behave erratically is for the
      mind to make a trivial mistake, such as in generating
      the series initiated by 3: 3, 6, 9, 12, 15, etc, the
      mind mistakenly produces the following, 3, 6, 8, 12,
      15 etc. So if the mind is like an error free computer
      or machine, then no randomness at all would be
      involved in generating the primes. From a physical
      viewpoint, the Riemann hypothesis roughly states that
      the irregularity in the distribution of primes only
      comes from random noise. Here, the random noise is
      the error rate of the mind.

      I believe I can prove both 1 and 2. Would this be
      enough to prove the RH?

      Essentially, one can prove the RH using concepts from
      above or from under it. The common way today is to
      use advanced math concepts. If such proof is ever
      possible, it would be understood by very few. The
      alternative way, which may be the real way, is to
      prove it using concepts that is more fundamental than
      the RH. Such concept concerns directly the essence of
      primes or the real definition of primes. If the
      essence of primes says that prime is unpredictable,
      then of course primes should give a chance appearance.
      If the essence also says that primes are 100%
      lawfully generated where randomness is completely
      ruled out, then of course, primes would show extreme
      regularity. Simply put, besides unpredictibility,
      everything else about primes is as lawful or regular
      as it can possibly be, limited only by the random
      noise of the mind.

      So if the essence of primes is like the above, then
      the RH is merely a manifestation or prediction of the
      essence. The essence automatically takes care of the
      RH or proves it. The RH is also a prove of the
      essence. A fundamental law or essence gives many
      predictions whose verification proves the law or
      essence. The RH is a deduction of the prime essence
      and is in turn a proof of the essence. If what the RH
      means can be independently stated in other ways, the
      RH is proven. That other way is to find the essence
      of primes, which is the 2 statements above.

      What Werner Sands said about primes being or meaning
      FIRST is right on target on the essence of primes.

      Thanks,

      Shi



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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
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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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