Re: [PrimeNumbers] Re: proving the Riemann hypothesis
- --- 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
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.
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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?