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

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• ... 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
>

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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• 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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