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Message from discussion first counterexamples in Riemann Hypothesis because Euler encoding is not viable #1349 Correcting Math

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More options Dec 30 2010, 9:44 pm
Newsgroups: sci.math, sci.physics, sci.logic
From: David Bernier <david...@videotron.ca>
Date: Thu, 30 Dec 2010 21:44:53 -0500
Local: Thurs, Dec 30 2010 9:44 pm
Subject: Re: first counterexamples in Riemann Hypothesis because Euler encoding is not viable #1349 Correcting Math

Archimedes Plutonium wrote:
> On Dec 30, 11:38 am, Archimedes Plutonium
> <plutonium.archime...@gmail.com>  wrote:
>> On Dec 30, 5:09 am, Archimedes Plutonium

>> <plutonium.archime...@gmail.com>  wrote:
>>> On Dec 30, 1:03 am, Archimedes Plutonium

>>> <plutonium.archime...@gmail.com>  wrote:
>>>> On Dec 29, 2:22 am, Archimedes Plutonium
>>>> <plutonium.archime...@gmail.com>
>>>> wrote:

>>>> (snipped to save space)

>>>>> In Circumferencing the Perimeter we start with a square-side and find
>>>>> its perimeter and then
>>>>> we pi-twiddle and see if we can match it with a circumference. We have
>>>>> truncations also.

>>>>> 215.50
>>>>> 2152.050

>>>>> Here is an example of on square side in the Circumferencing the
>>>>> Perimeter:

>>>>> Let me try 2152.550 as more suitable
>>>>> side of square =  2152.550
>>>>>  perimeter = 4xside = 8610.200
>>>>>  8610.200/3.141 = 2741.228 = diameter
>>>>>    start pi twiddling 1/(B^2)twiddle 8610.200/2741.228 = 3.1410010
>>>>> pi twiddle = 3.141002
>>>>>  3.141002 x 2741.228 = 8610.202 mismatch
>>>>> 3.141001 x 2741.228 = 8610.199 mismatch

>>>>> Can someone set up a computer program that incorporates the above
>>>>> example and find that
>>>>> accurate table of first breakdowns in B matrices from 100 to 10^8?

>>>>> Is 215.50 the first square-side to have a breakdown in the 100 B
>>>>> matrix? Please fill in the
>>>>> first breakdowns all the way out to 10^8.

>>>>> P.S. Can someone set up a computer program to tell me all of the even
>>>>> cube roots of integerized pi lie? 314 is integerized pi to three
>>>>> places and 3141 is integerized pi to
>>>>> four places and neither are evenly cube rootable. I want to know along
>>>>> the integerized pi
>>>>> string of digits, where it is evenly cube rootable. I suspect that pi
>>>>> is cube rootable only
>>>>> at the 603rd digits where pi has those three zeroes in a row. The
>>>>> reason I want this information is because pi could tell us where the
>>>>> first counterexamples to FLT exist when
>>>>> we have infinity as imprecisely defined. In other words, pi could lead
>>>>> us to how large of a
>>>>> large number we have to go to in order to engineer the counterexample.

>>>>> Or, pi may tell us that 10^603 is the counterexample of FLT for
>>>>> exponent 3.

>>>> So are those accurate?

>>>> 215.50 first breakdown in 100 B matrix
>>>> 2152.050 first breakdown in 1000 B matrix of Circumferencing the
>>>> Perimeter

>>>> And can someone fill in the table out to 10^8 B matrix?

>>> 215.50
>>>  2152.050
>>> 21521.5000

>>> Circumferencing the  Perimeter:
>>> for B matrix 10^4
>>> side of square =  21521.5000
>>>   perimeter = 4xside = 86086.0000
>>> 86086.0000/3.1415 = 27402.8330 = diameter
>>> start pi twiddling 1/(B^2)twiddle 86086.0000/27402.8330 = 3.141500004
>>> pi twiddle = 3.14150001
>>> 3.14150001 x 27402.8330 = 86086.0001 mismatch
>>> 3.14150000 x 27402.8330 = 86085.9998 mismatch

>>> Apparently the digit pattern arrangement of 215---- leads to
>>> breakdowns in Circumferencing, but whether they are the
>>> first breakdowns for those B matrices is not yet established.

>> I think I may have spotted where the Riemann Hypothesis has its first
>> breakdown in
>> counterexamples of nontrivial zeroes on the 1/2 Real strip. The
>> question being, as in
>> FLT, whether the breakdown is before 10^603 or long after the 10^603
>> as the border between
>> Finite and Infinity.

> Reading from the book Prime Obsession by John Derbyshire on page 104.

> What I am trying to resolve is whether the Euler encoding of the
> multiplication of primes is really and truly equal to that of the zeta
> function of the addition series.

The Riemann-von Mangoldt formula for psi(x) is a truly marvelous thing.

First, the definition of the von Mangoldt function Lambda(n),
for an integer n >=1:

If n has no prime factors, Lambda(n) = 0.
If n has two or more distinct prime factors, Lambda(n) = 0.
The remaining case is where n has just one prime factor, p.
Then n could be p, p^2, p^3, ...

Then Lambda(p) = Lambda(p^2) = Lambda(p^3) = ... = log(p) [base 'e' ].

psi(x) :=  sum_{1 <= n <= x} Lambda(n) .
[ This is the summatory von Mangoldt function, or Chebyshev function,
according to Wikipedia].

There is an expression for psi(x) in terms of the non-trivial zeta zeros
that is referred to as the "Riemann-von Mangoldt explicit formula"
or "von Mangoldt explicit formula".  You can find it here,
following the text "Von Mangoldt's formula for psi(x):"
< http://web.viu.ca/pughg/Psi/ > .

There is also an applet there.  As more zeta zeros are included,
the graph changes less and less.  I think there are jump
discontinuities in psi(x) at primes and prime powers,
and I'm not sure how the "explicit formula" behaves point-wise
at the jump discontinuities.

David Bernier

> Here is what we do know for sure, is that pi is a series involving
> primes and this series allows us to
> fetch three zeroes in a row in the 10^-603 place value.

> But that a multiplication of primes as the Euler Encoding would not
> possibly be able to fetch 3 zero digits in a row
> in multiplication. So that the Euler multiplication encoding is not
> equal to the Riemann Zeta Function and that all this huff puff
> hallyballoo about the primes being as perfectly spaced as possible was
> just a fanciful wish.

> What I have to do here, is see if I can analyze where RH has its first
> counterexample, whether it is below the 10^603 mark or smack dab on
> the mark of 10^603 where Circumferencing the Perimeter breaks down
> also, or whether RH breaksdown some distance beyond the 10^603 mark.

> Archimedes Plutonium
> http://www.iw.net/~a_plutonium/
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies

--
\$ gpg --fingerprint david...@videotron.ca
pub   2048D/653721FF 2010-09-16
Key fingerprint = D85C 4B36 AF9D 6838 CC64  20DF CF37 7BEF 6537 21FF
uid                  David Bernier (Biggy) <david...@videotron.ca>