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From: Archimedes Plutonium on 16 Jul 2010 16:53


Archimedes Plutonium wrote:
> Archimedes Plutonium wrote:
> > Alright, so I have a method, now all I need are conjectures waited to
> > be conquered after
> > I sharpen my sword.
> >
> > So let me recap how the method works. I use Indirect Euclid Infinitude
> > of Primes which retrieves two new primes not on the list I started
> > with. I weave into the Indirect method the
> > Mathematical Induction in case the primes need identification as a
> > Euclid Number. This method proved the Infinitude of Mersenne Primes
> > and the Infinitude of Perfect Numbers.
> > So I take a peek at any other open conjectures of prime infinity.
> >
> > --- quoting in parts from Wikipedia with notes below ---
> >
> > Many conjectures deal with the question whether an infinity of prime
> > numbers subject to certain constraints exists. It is conjectured that
> > there are infinitely many Fibonacci primes[24] and infinitely many
> > Mersenne primes, but not Fermat primes.[25] It is not known whether or
> > not there are an infinite number of prime Euclid numbers.
> >
> > --- end quoting ---
> >
> > Fibonacci sequence and primes:
> >
> > 0,1, 1, 2 , 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
> >
> > 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, ....
> >
> >
> > Fermat primes F= (2^2^n) +1
> >
> > 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, …
> >
> > Euclid numbers
> >
> > The first few Euclid numbers are 3, 7, 31, 211, 2311, 30031, 510511
> >
> > --- end notes from Wikipedia ---
> >
> > Alright, the Math Induction was able to make the suppose true for N
> > case, able
> > to show that the N+1 case was another Mersenne form number of (2^p) of
> > the
> > (2^p)-1.
> >
> > Can I do the same for Fermat primes of form (2^2^n) +1? In other
> > words, if I suppose
> > true for the case N that Euclid's Number without the adding of 1 or
> > subtracting of 1
> > is another form of (2^2^n), then, just like Mersenne primes I will
> > have proved an
> > infinitude of Fermat primes. Quite honestly I think I can show that
> > via Math Induction
> > with the suppose for case N that the Euclid Number is (2^2^n) that the
> > case N+1 can be
> > finagled to be another form of (2^2^n), the reason I say this is
> > because we can reiterate
> > the primes listed in the sequence as many times as we like and when we
> > divide them into
> > Euclid's Number they still leave a remainder. For example, if 2,3 are
> > the only primes that exist
> > and I set up Euclid's Number to be (2x3x2x3x2x3x2x3...) then either
> > add 1 or subtract 1, the
> > division by 2 and 3 will still leave a remainder of 1. So in the case
> > of Fermat's primes, it looks as though the Math Induction delivers a
> > Fermat's prime for the N+1 case. And thus Fermat's
> > primes are infinite, contrary to what Wikipedia wrote.
> >
> > As for Prime-Euclid-Numbers they are infinite set by the trivial proof
> > from Twin Primes being
> > infinite. So the proof is trivial since Twin Primes are infinite.
> >
> > As for the Fibonacci primes, I do not see them fitting into a Math
> > Induction template. So I am
> > going to sleep on this one.
> >
>
> Take my words back, I remembered something recursive with the
> rectangles
> and that the Fibonacci numbers generated Pythagorean triples.
>
> --- quoting from Wikipedia ---
> Any four consecutive Fibonacci numbers Fn, Fn+1, Fn+2 and Fn+3 can
> also be used to generate a Pythagorean triple in a different way:
>
> --- end quoting ---
>
> So it looks good for a Math Induction to identify the N+1 case as a
> Fibonacci number
> but careful in what the N case is supposed. Of course the overhanging
> Indirect Euclid
> IP will ensure the Fibonacci number is prime.
>
> So we are beginning to see the huge power that this team gives for
> clearing out all prime
> conjectures whose question mark is, is the set finite or infinite?
>
> Had anyone made a count as to how many conjectures of prime set
> infinite were outstanding?
> Was it in the hundreds, perhaps thousands of unsolved infinity of
> primes conjectures.
>
> But I wish most people would apply a little commonsense to these open
> conjectures, such as the case of Fermat's primes of form (2^2^n) +1.
> Since the Polignac Conjecture is proved true
> we can reach a point where N +2k of the separation between two primes
> is far greater than
> the separation of (2^2^n).
>
> Now if I have time I would like to discuss a mental picture of how to
> picture infinity as what
> the old math implies what infinity looks like since they are derelict
> in defining a boundary
> between finite and infinite at 10^500. We can all mentally picture
> 10^500. But I would like to spend time on a picture of infinity that
> the Old Math was belaboring under and which would easily clear up the
> idea of how big (2^2^n) is in relation to infinity. And the picture I
> give of
> Infinity as how Old Math portrayed infinity can point out the flaws of
> that viewpoint, and why
> the 10^500 system is so superior to Old Math.
>

Old Math never defined with precision what it means to be a finite-
number and left
it ambiguous as to whether a number was a finite-number or an infinite-
number.
Around 1899 and 1900 and 1901 Kurt Hensel came up with what he called
p-adics
which were a strange new set of numbers. All of them were infinite-
numbers. And until
the 1990s when I pointed out that the Natural Numbers were actually
the p-adics
since there was nothing in the Peano Axioms to ward off that
conclusion. Then I
invented my own infinite integers since I detested the operations on
Hensel p-adics.
My AP-adics were just the Peano Natural Numbers, and what happens with
the
Peano axioms when no boundary is drawn between finite-number and
infinite-number.

What happens to math itself is that math is destroyed when it cannot
precision define
finite-number versus infinite-number. Algebra builds up slews of
unproveable problems such
as FLT, Riemann Hypothesis etc etc. In fact, there are more unproven
problems in Number
theory than there are proven problems in Projective Geometry.

But let me give you a picture of Infinity in words when Mathematics
does not do its job of
precision defining.

In the AP-adics the finite numbers would all have a string of digits
ending in the leftwards
string with digits of 0s. So that the number 2010 is the number
0000....00002010. So all
of mathematics that is written in textbooks and preached upon in
college and universities
are numbers that look like this 0000....0000xyz. Trouble with that is
the number
002222....3333 would also be considered finite-number and be relevant
to FLT and Riemann
Hypothesis, only we all recognize that it is far different from a
number like 22333 or any other
string of 2s and 3s we call finite-numbers. So the Old Math assumed
the definition of Finite-Number as numbers that ended in a leftward
string of 0s. But that falls apart as just explained.

So what is the full extent of infinite-numbers, given that finite-
numbers are somewhere in between 0009999...99999 and 0 ?

Well it looks as though the number 99999....99999 is the largest
number possible with
9999.....99998 as the second largest. But this is not true, because
with infinity means no end
unless infinite-numbers are defined with a boundary.

The thing about infinity when you apply Physics to it, you must have a
duality and you cannot have just the concept of "endless" alone. The
duality concept is place-value. So that 9999....9999 is not the
largest because then you have another larger number of 1111....11111
which has 9999.....99999 place value. What this allows is that you
have every number written up as a single number where you have a
Champernowne's number of every number
as such .........131211109876543210 which includes all the infinite
numbers themselves inside
that single number.

Is your head dizzy yet? This is what happens to math when you refuse
to give a boundary
between finite and infinite.

What happens with infinity that is unbounded, then you can start to
create numbers that violate every mathematics theorem ever proved. One
of those theorems is that 2 is the only even prime number. Well, with
infinity unbounded I can create successive numbers, Peano Natural
Numbers a string of say 50 successive Natural Numbers all of them even
with no odd number
in between and all of them prime numbers.

Sounds impossible, you say?

Actually very easy as I take a Champernowne number and alter the one
end as the other end
is being divided by 2

But all of this is very simple to see in Old Math itself, because Old
Math recognized another
crisis point in definition. A point where Old Math could not even
exist unless it laid down a
boundary and that crisis point was division by zero. Zero, by the way,
is the inverse of Infinity,
and we must restrict the definition of zero or precision define zero
when dividing by zero that the answer is "undefined". Because any
other definition of zero dividing we can have 2 = 3.

Just as I said that with infinity unbounded I can craft any number you
like that destroys any
proven theorem you like. I can construct infinite numbers that are
neither composite nor prime.
I can construct transcendental counting numbers. Just as dividing by
zero, I can destroy any
axiom or theorem of Old Math.

So what started this conversation about Infinity? I was wanting to
relate to how big infinity was
compared to a number like the Fermat primes? Primes of form (2^2^n)
+1. Well in Old Math
where finite-number is never defined, the Fermat primes would be
somewhere along this
line of numbers

00000000.....99999

Would be somewhere along that line of 9s digits, nowhere even close to
the other infinities
of 1111......00000 or 222......00000 then the 3s infinities then the
4s infinities all the way
to the 9s infinities.

So all of Old Math was stashed away into a tiny piece of the 0s
infinity, even the Cantor
infinities was not even breaking out of the 0s infinity, for the
Cantor infinities did not
threaten to destroy Old Math but hoped to be a part of the Old Math.

So, when mathematicians recognize they failed in their job, failed to
define the boundary
between finite-number versus infinite-number, then all of Old Math is
destroyed, just as
all of Old Math is destroyed when dividing by zero is used.

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
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