## proving the Riemann hypothesis

Expand Messages
• The Riemann Hypothesis essentially says that the primes are as regularly distributed as possible. The mathematician Enrico Bombieri put it: “If the Riemann
Message 1 of 40 , Feb 1, 2007
The Riemann Hypothesis essentially says that the
primes are as regularly distributed as possible. The
mathematician Enrico Bombieri put it: If the Riemann
Hypothesis turns out to be false, there will be huge
oscillations in the distribution of primes. In an
orchestra, that would be like one loud instrument that
drowns out the others - an aesthetically distasteful
situation."

If the RH is false, the gap between prime P1 and the
next prime P2 could be anywhere from 1 to infinitely
large. The gap would be a random number from 1 to
infinity. To prove the RH true, we only need to prove
that the gap is not without a consistent or fixed
upper limit. I have found a simple proof for this
that could be understood by anyone above the level of
elementary school. I am writing it up for
publication. 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.

Can anyone else also prove this? If this can be
proven, would it represent a proof of the RH? The RH
is merely a special manifestation of the regularity of
primes. This regularity could be manifestated in
other ways. A proof for any one of these
manifestations would prove the regularity of primes,
which in turn would take care of all other
manifestations. The regularity of primes is the
foundation, which give rise to the RH. Any proof for
the regularity is a proof for the RH. A direct proof
of the specific statement of RH (all zeros are on one
line) may indeed be impossible. It may have to be
proved from a totally different perspective. As
Einstein put it, a problem cannot be solved by the
same mindset that created the problem.

I would further conjecture that the gap must be
smaller than the value of P1, but I have not been able
to prove it.

____________________________________________________________________________________
Have a HUGE year through Yahoo! Small Business.
• 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
Your message has been successfully submitted and would be delivered to recipients shortly.