Archimedes Plutonium wrote:
>
> I believe we can prove the Riemann Hypothesis is false by a
> paralleling of primes of form where they
> are primes and an infinite set, but which they are so spread far apart
> that we only find the first such
> prime of that form that we would believe they are like the Riemann
> Hypothesis that all the nontrivial
> zeros are on the 1/2 Real line.
>
I believe the above is an alternative equivalent statement of the
Riemann Hypothesis. What it implies is
that if the Riemann Hypothesis were true, then we come to a point of a
"Prime form" wherein those
primes are no longer an infinite set and any prime forms beyond this
prime form are also finite sets.
There are only 45 known Mersenne Primes, and the proof that Mersenne
Primes are finite or infinite has
eluded mathematicians. I have recently given a method of proving
Mersenne Primes are infinite sets
in Natural-Numbers = Infinite Integers. This same method would easily
prove that Mersenne Primes
raised to the power of Mersenne Primes FORMS is also a form that is an
infinite set of primes.
So, if the Riemann Hypothesis is true, then we arrive at a FORM of
primes in Natural-Numbers = Finite
Integers for which those primes are a finite set and cannot be
infinite set and also, all forms beyond that
initial Riemann Hypothesis-Form are finite prime sets. So if the
Riemann Hypothesis is true, then
near the Mersenne Prime Form is a finite set and not infinite and all
higher forms beyond the Mersenne-Form
are also finite sets. So if the Riemann Hypothesis is true, means that
somewhere out there, perhaps
the Mersenne primes or a form slightly higher than Mersenne Primes do
all those forms have only
a finite set of primes and no more prime sets that are infinite in
cardinality.
So I think that I have linked the truth or falsity of the Riemann
Hypothesis with the FORM of primes and
their set cardinality.
If the Riemann Hypothesis is false, then, no matter how extended the
Form of prime-- say we have
Mersenne primes raised to the power of Mersenne primes or say we have
2 raised to successive powers subtract
1. No matter how attenuated or thin it is for a Prime Form, that Form
is an infinite set of primes.
So if you believe the RH is true, then there is a Form in which the
primes of that Form are finite and all higher
forms are finite. But if you believe RH is false, then no matter how
extended of a Form of primes, they are
still infinite set of primes that make up that form.
And the geometry equivalent is that the Riemann Hypothesis is lines of
latitude and those lines are formed
by an infinite set of numbers. The lines of latitude is infinite set
of latitude lines and the points on the
latitude lines are all infinite sets.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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