easier proof of Prime distribution x/Ln(x) #481 new book 2nd edition: New True Mathematics

[plutonium....@gmail.com]

Below is a post I made earlier today. It occurred to me that
the below offers an easier proof of the Prime Distribution
of x/Ln(x) by use of the Perfect Square Distribution x/sqrt(x).
Of course, it requires FrontView with BackView and the
AP-adics. But also, it is true for the AP-Reals between
"whole number intervals".

--- repeat of earlier post today ---
One thing I am going to do as a summary of this book since the next
time
I pick up this book with the 3rd edition is to make a summary list at
the
end of what changes I had made to remember when I pick up on the
3rd edition. Things like concave outward and concave inward so as to
fit Hyperbolic alongside Elliptic on the same sphere. And things like
dropping rightwards and leftwards. A summary list at the end to jog
my memory when I start this book anew since many of the items were
thrown out.

But an intriguing development occurred along the way for AP-adics
in what of the Primes theory is retained and what is changed. And
the idea came that Perfect Squares follows a similar pattern as
the distribution of primes where one is x/sqrtx and the other is
x/Ln(x)

The intrigue is that I have all the +AP-adics between 9999....99999
and 000...000 and ask whether the old formula of x/Ln(x) still
holds true? I showed a way of finding the largest primes in existence.
But I used x/Ln(x) to find these primes. The idea was simple, in that
9999....9999 cannot be prime since the leading two digits 99 are not
prime. Then the leading three digits 999 are not prime.
So the pattern was that the smallest leading digits of 97 was prime
so the largest prime number from 0 to 9999...9999 had to start like
this 97......97

Here is what I wrote some months earlier:
Obviously 97 is relatively prime from 0 to 100 so now I want the next
digit of
97- and what occupies that next spot? So I look in the list of primes
for a
prime of 97- and I find 977 is prime, then I next look for a prime
977- but find
none in the list, so I jump to looking for a prime of 977-- and there
is a prime
as 97789, now I look for a prime of 97789- and we have 977897 and that
is about all I feel like fleshing out of the world's largest prime
number
977897...........

Now from the BackView is easier since I can fill it in with:

977897.....999997

Now Tim Little interceded with the question of why I thought x/sqrtx
for Perfect Squares should follow a pattern of x/Ln(x). And I gave a
answer to that saying that they are related since Primes versus
Composites occupy all the numbers and thus perfect-squares are
a subset of composites. So they are related, however minutely as
for example the number 101 is not a simple 100/10=10 but that tiny
bit of extra in 101/sqrt101 is related to a Ln(101). But that aside.

Let me discuss the relationship of Perfect Squares to the distribution
of Primes. Let me take as solid knowledge x/sqrtx and play around
with x/Ln(x).

If the largest integer is 999...9999 before the South Pole at
1H000..000
and the South Pole is obviously composite, but is the next point
1H000...0001 prime?

Now we do not have 1H000...000 = 1000...0000*100...0000
since that is 10% x 10% not equal to 100%
But we do have 1H000....000 = 1H000...000 * 1H0000...0000
So the sqrt of 1H000...000 is itself and implying that the next
number in succession 1H000...0001 is most definitely a prime number.

So let me use x/sqrtx to pursue the primes question. How many primes
exist between 9999...9999 and 0 ?? Well, it stands to reason that
since
there are vastly fewer Perfect Squares from 100 to 0 in that of only
ten
and there exists 25 primes in that same interval.

That we can expect there to be only 10%- relative-at-most of the
numbers from
9999...99999 to 0 to be perfect-squares and expect that 25%- relative-
at-most
of those numbers from 9999...9999 to 0 to be Primes.

So here I find myself in a position where I can confirm the
distribution of primes
by simply checking upon the distribution of numbers that are Perfect-
Squares.

So what is the world's largest Perfect Square? A number between
9999...999
and 0. Obviously it is going to be 999...9999 * 9999...9999

99 x 99 = 9801
999 x 999 = 998001

so the pattern becomes clear

999...999 * 999....9999 = 9999...99800...00001

That is the world's largest Perfect Square given the space of
999...999 to 0

And that would agree with the world's largest prime number as that of

977897.....999997

Here is a beautiful confirmation that Primes follow x/Ln(x) simply
because
the square root operation on 999...999 to 0 follows how we take square
roots or how we do the operation of "squaring". So the operation of
square
root or squaring in mathematics forces the Primes to be x/Ln(x)

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

[plutonium....@gmail.com]

I am still amazed by how this little step, this little one step can
change
everything in mathematics of number theory. Instead of starting with
Naturals to build Rationals, we start with Reals and build Real-
Rationals.

The old math could never do this because they did not have FrontView
with BackView. But we can.

We say there exists a number 0d0000...0000 and then say there
exists 0d000...0001 and then add infinitely many times to yield
all the Reals. So this is a Real 8d7777....66666 and is obtained
through the infinite adding of 0d000...0001.

Now we go one step higher for we have the Reals as this matrix:

0d000...0000
0d000...0001
0d000....0002
etc etc

And we place each number as a numerator to every number as
a denominator. We have all possible arrangements of Reals as
both numerator and denominator.

So unlike the Old Reals which had the Rationals as a subset. Here
we have the Rationals as a larger set than the Reals themselves.

Then we build the Irrationals as Continued-Fractions.

Since these Irrationals are dense and topologically connected, we
never need transcendental numbers. There is no higher category
than that of dense topologically connected. So the Transcendental
numbers were just figments of the imagination. Pi and "e" were not
algebraic, but rather were simply imaginary as was "i" in Reals or
were two strange numbers that were "incompletely developed".

So in the AP-Reals we need only two of these strange numbers of
"pi and e".

Now I bet in mathematics there have been other subjects where a simple
change of the "starting set" yielded a vast new vista of opportunity.
So when
we start with the Reals instead of the Naturals we end up with a
better
number theory. Now physics has examples of this "better starting
points".
In the case of temperature, it is better to start with "absolute zero"
than
to start with an arbitrary assignment of water at 32F and 212F. Or
take the
case in physics when you start with the Earth as the center of the
Solar
System rather than the Sun. Or, I suppose in mathematics, take the
case
where you start with the premiss that given a line and a point not on
the line
there is one and only one line parallel to given line.

So it really matters where our starting point is on a theory. And if
we start
with Naturals and build Rationals or start with Reals and then build
Rationals, we have a whole new different mathematics.

The AP-Reals are more simple, are countable, and have a better
algebra.

[plutonium....@gmail.com]

Now there is a possible way of showing that the AP-Reals are the true
Reals
instead of the Old Reals. It is how well the AP-Reals can do Calculus.
If I have
my notions correct, the Calculus really only needs a "dense set" and
does not
need the topologically connected set that is the AP-Reals-Rationals-
Irrationals.

If I have my notions correct about this then functions like sin(1/x)
are not discontinuous
as approaching 0, where every value is computable since the AP-Reals-
Rationals
are dense. And functions that are
continuous everywhere but differentiable nowhere are more easily
visualized
as jagged peaks.

If I have my notions correct, then the Calculus is built solely on the
AP-Reals-Rationals
and no need for the AP-Reals-Rationals-Irrationals.

Whereas in Old Reals, they had to go all the way out and embrace
transcendental
numbers, whereas in AP-Reals, we drop the irrationals and the
transcendental are
nonexistent.

I am not expert enough to sort out what the AP-Reals will do to the
various forms
of integration and differentiation, but there is no need for the
"limit concept" in
AP-Reals, because the formation of Rationals and Irrationals is the
limit concept
already incorporated.

[plutonium....@gmail.com]

[plutonium....@gmail.com]

Hit the wrong key and sent a post prematurely.

Let me discuss the Dedekind program in Old Reals, in that you need it
because you started with the Naturals and then expanded into
Rationals,
Irrationals and then had to expand once more to get transcendentals.

But the beauty of AP-Reals is that we start with the Reals in tact, up
front.
We then do a Rationals on the AP-Reals and get AP-Reals-Rationals.
And
finally we do a AP-Reals-Rationals-Irrationals. This means that there
are
no Transcendentals and that the Dedekind Program ends with the
AP-Reals-Rationals-Irrationals since it is dense and topologically
connected
and closed to all operations.

Is there a AP-Reals-Rationals between any two given AP-Reals-
Rationals?
I need to find a way to shorten these terms such as AP-Reals-Rationals-
Irrationals.
But the answer to the question is yes, they are dense. And the
question, is
there an AP-Reals-Rational between any two AP-Reals-Rational-
Irrational? And
the answer is affirmative again. And affirmative for a AP-Reals-
Rational-Irrational
between any two AP-Reals-Rational-Irrational.

So we crowded out the Transcendental Numbers. We made them obsolete
and
no need. Quite plainly, they never existed. And, mathematics really
only had two
of them-- "pi and e". But a better description of pi and "e" is not
that they are
algebraic or non-algebraic but that they simply are two special
numbers that are
not having a completed or grown digit string, for they are "growing
numbers"
and dependent on the Physics Clock of the Cosmos as to what the next
digit is
for "pi and e".

So it is rather neat how the AP-Reals dispenses of alot of nonsense in
the Old
Math, and dispenses it by starting not from Naturals as the initial
starting off
set, but rather, starting from the entire Reals as "All Possible Digit
Arrangements".

The history of human thought had another experience similar to the AP-
Reals. Instead
of starting off astronomy with a geocentric (Earth the center of the
Cosmos), instead
of starting astronomy off with a poor choice as the Earth the center,
we start off
astronomy with a Solar System that has the Sun as its center. So a
shift, a change
with our starting set, hugely affects the science enterprise.

[hanson]

<plutonium....@gmail.com> wrote:
I hit the wrong key and sent a post prematurely.
[Don't worry. Did you a favor: snipped you crap]
>
hanson wrote:
... ahahahaha... why should anyone expect anything
different from you, you Archie being the poster child
for an unsuccessful used-vacuum-cleaner salesman?
But carry on. Don't let me cramp your style.
Ttanks for the laughs... AHAHA... ahahahahanson