## Re: [PrimeNumbers] Re: proving the Riemann hypothesis

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• ... So proving the RH would prove that primes are both random and non random, which is the key property of being a prime or what make it interesting. The RH
Message 1 of 40 , Feb 2, 2007
>
> So RH still allows for a good deal of "randomness"
> in
> the distribution of the primes, but it states that
> the
> maximum deviation of pi(x) from Li(x) is
> proportional
> to sqrt(x)*log(x).
>
>

So proving the RH would prove that primes are both
random and non random, which is the key property of
being a prime or what make it interesting. The RH is
meant to prove what we suspected of primes is true.
If we can prove the yin yang duality of primes without
using the RH, we basically would accomplish the same
thing. Prove the duality of prime is the real goal
and the RH is just one way of doing it. There may
exist simpler ways. May this characterization of RH
represent a reasonable assesment of the RH?

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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
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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