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From: Archimedes Plutonium on 9 Jan 2010 22:10


Archimedes Plutonium wrote:
(snipped)
>
> Now that also sheds light onto a bigger and major question. Once we
> confine all
> of Mathematics to the Planck Unit of 10^500 and its inverse, then the
> proof of
> conjectures such as Riemann Hypothesis take less than a day for a
> supercomputer
> to reveal that RH is true for 10^500 and its inverse and thus true for
> mathematics.

Well RH is far more complex than simple multiplication of pi x e to
the 10^-500 decimal
place value. RH, as it turns out has been verified by computer to only
about 10^13 or
thereabouts. But I am not sure of what is to be deemed as 10^500 in
the Riemann Hypothesis? Do we verify to the number 10^500 or to the
first 10^500 nontrivial zeroes?
So I am a bit cloudy on what is the 10^500 in the Riemann Hypothesis.

--- quoting from: ---
http://www.zetagrid.net/zeta/rh.html

What have we achieved so far?

The result of the computation which verified the first 100 billion
zeros of the Riemann zeta function confirms the calculations made
previously by "other scientists" and extends these to the first 100
billion nontrivial zeros. All these zeros of the form + it have real
part = 1/2 and are simple. Thus, the Riemann Hypothesis is true at
least for all |t| < 29,538,618,432.236.
More details about this computation will soon appear in a paper.

--- quoting the reference "other scientists" in the above quote ---
RESULTS CONNECTED WITH THE FIRST 100 BILLION ZEROS OF THE RIEMANN ZETA
FUNCTION (DRAFT)
SEBASTIAN WEDENIWSKI
ABSTRACT. This report presents the results of recent and ongoing
internet computing inside the intranet of IBM Corporation which
required 1.3 . 1018 floating-point operations: the first 100 billion
nontrivial zeros of the Riemann zeta function (s) are simple and lie
on the line Re(s) = . Thus, the Riemann Hypothesis is true at least
for all |Im(s)| < 29, 538, 618, 432.236.
Date: August 1, 2002

--- end quoting from "other scientists" ---

So maybe we have many years or centuries to wait before we can verify
the truth of RH to
that of 10^500.

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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