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Re: proving the Riemann hypothesis

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  • jbrennen
    ... You really *can t* prove that primes cannot be predicted. The set of primes is deterministic, and the primality of X, or the next prime after X, or the
    Message 1 of 40 , Feb 2, 2007
      --- Shi Huang wrote:
      >
      >
      > > 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.

      You really *can't* prove that primes cannot be predicted.
      The set of primes is deterministic, and the primality of
      X, or the next prime after X, or the previous prime to X --
      any of those can be determined in a finite amount of time
      using very simple algorithms and finite storage resources.
      Now of course, it is computationally infeasible to determine
      the next prime after 10^(10^100) due to physical restrictions
      on computers, but proving or disproving RH won't change that.

      >
      > Proving the RH will prove that primes are bound by
      > laws...
      > ...snip...
      >

      The Prime Number Theorem already proved that. RH is notable
      for three basic reasons (IMHO) -- it is almost certainly true (a
      tremendous amount of empirical evidence points at its truth),
      it bridges the gap between number theory and complex analysis,
      and its proof would "tighten" the laws on prime distribution
      to the point where a whole bunch of other results would become
      possible. Heck, mathematicians aren't even waiting for RH
      to be proven -- there are a whole bunch of published results
      which are only valid if the truth of RH is assumed.

      Jack
    • 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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