> To the extent that I can understand what you're

If it remains unknown whether primes can be predicted,

> saying, I

> think that the "yin yang duality" of primes is

> already proven.

>

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.

____________________________________________________________________________________

Don't get soaked. Take a quick peak at the forecast

with the Yahoo! Search weather shortcut.

http://tools.search.yahoo.com/shortcuts/#loc_weather- 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