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From: plutonium.archimedes on 3 Sep 2009 10:11
> On Sep 3, 12:04 am, "plutonium.archime...(a)gmail.com"
> <plutonium.archime...(a)gmail.com> wrote:
(snipped)
Google is not working properly, so the followups on Google
are meager.


>
> > So that the Prime Number theorem of x/Ln(x) and the
> Riemann
> > Hypothesis, no longer hold true for Standard Math
> of its
> > infinite-interval of pure composites. For that solo
> interval must
> > be at the so called point-at-infinity just before
> the last and
> > largest prime.
>
> Unfortunately, I still don't follow. I thought the
> point of
> the Infinitude of Primes proof is to show that there
> is _no_
> last and largest prime.
>

I have a problem with words to describe the situation,
and too bad that "end" means last means terminal
and they all mean about the same thing. But it is not
the meaning I was trying to convey. I was trying to
convey "last and largest in an interval"

Let me try that again with an analogy of 0 to 100
compared to all the Infinite Integers from 0 to
9999....9999, South Pole = 1000...000

From 0-100 we have 25 primes as per x/Ln(x)
and we have the last and largest prime as 97.

From 0-999....99999 we have primes to obey
the Riemann Hypothesis and to obey x/Ln(x).

Now we do a switcharound and require
the x/Ln(x) to tell us not the distribution of primes
but to tell us of a maximum interval of pure
composites. In 0-100 this interval is 89 to 97 for
a length of 7.

From 0-infinity in Finite Integers, according to
x/Ln(x) there must exist at least one of these
intervals of pure composites according to
infinitude of primes proof.

Contradiction, since you cannot have these items:
1) infinitude of primes
2) infinitely long interval of pure composites
3) Prime Number theorem x/Ln(x)
4) Riemann Hypothesis
5) Naturals = Finite Integers

You cannot have those five and be noncontradictory

You can have these five:
1) Infinitude of Primes
2) infinitely long intervals of pure composites
3) Prime Number theorem
4) Riemann Hypothesis
5) Naturals = Infinite Integers

LWalk, we can say that in the interval 0-100 that 97 is the last and
largest prime.

We can also say that in the interval 0-9999...99999 that a prime
of 9999..799.... is the last and largest prime from the interval
0 to 9999....99999

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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