Science > Physics > #8# new book "Correcting Present Day Mathematics and Setting...." (8) proving Infinitude of Twin Primes and other proofs
| Topic: |
Science > Physics |
| User: |
"a_plutonium" |
| Date: |
30 Jan 2007 01:54:08 AM |
| Object: |
#8# new book "Correcting Present Day Mathematics and Setting...." (8) proving Infinitude of Twin Primes and other proofs |
Listing some of the chapters of this new book:
"Correcting Present Day Mathematics and Setting it on Course for the
Next 2 Millenium"
a_plutonium wrote:
Correcting the Logic of these mistakes in mathematics
(1) Infinity exists in only one unique form, and proof thereof
(2) Peano Axioms are gap ridden and self contradictory
(3) Euclid Infinitude of Primes proof, Indirect Method
Proof of most of the World's unsolved Math Problems due to the fact
that Natural Numbers are these 0,1,2,3, ...., ...999999
(4) Riemann Hypothesis
(5) Fermat's Last Theorem
(6) generalized FLT (known as Beal's conjecture)
(7) Goldbach Conjecture & hundreds of the Erdos problems in Number Theory
(8) Infinitude of Twin Primes and Quadrapole Primes
(9) Infinitude of 4-primes, 6-primes, 8-primes,....
(10) Infinitude of Perfect Numbers
(11) Infinitude of primes of form (2^n) +1
(12) the number 1 is the only odd perfect number
I will prove those above listed 4-12 by the key fact that the
Natural-Numbers are this set:
0 , 1, 2, 3, 4, 5, 6, 7 , 8 , 9 , 10 , 11, ........., .....9999996,
....999997, ......999998, .....9999999
I will also prove these unsolved problems of mathematics:
(13) Kepler Packing
(14) 4-Color-Mapping
(15) 2-Color-Mapping
(16) Poincare Conjecture
(17) NP Problem
And demonstrate what I feel is my best contribution
to mathematics theory that geometry has instrinsic
numbers as coordinates and that geometry is
unified and a mirror reflection of physics
(18) Riem geom union Loba geom = Eucl geom
(19) and because numbers form geometry and likewise, geometry forms
numbers that this is true:
positive Adics union (negative Adics) = Reals
I am going to combine (8) and (9) above into one chapter. For they are
related
and the proofs are brief.
It was impossible to prove infinitude of twin primes in the old
alleged Natural-
Numbers and the reason being is that it was impossible to set up a
Euclid
type argument proof. That both W-1 and W+1 in a Euclid argument are
twin primes in reductio ad absurdum. But since it cannot be
constructed
into a proof of twin primes has a good reason and the reason is that
the
Natural Numbers are this set 0,1,2,3,......, 9999....99999. With the
full
set of Natural Numbers in view, then Twin Primes or 4-primes or 6-
primes
are all easy to prove their infinitude.
And the technique of proving them infinite is a new technique and
highly
beautiful.
Proof of Infinitude of Twin Primes (2-primes):
We look for a irrational-infinite-integer. Pi of the Reals
3.14159265....
when transposed into an Infinite Integer looks like this:
..........562951413
It is prime since it is irrational. Now I construct an Infinitude
of Twin Primes using that above Infinite-Integer as what can be
called its rootstock.
First pair of Twin Primes is .......562951413 and .........562951411
Second pair of Twin Primes replaces the 4 with 5
Third pair of Twin Primes replaces the 1 with a 2
Do you see how we construct an infinitude of Twin Primes from
a rootstock of a irrational Infinite Integer? We move up the string
and successively change a digit which does not affect the
irrationality
of the overall string of digits.
Proof of Infinitude of Quadrapole Primes: First let me note that this
is a new conjecture and new theorem to mathematics for before
these writings no-one heard of quadrapole primes in the Natural-
Numbers
nor to the most dense distribution of primes where you can almost
get primes so dense that after every even number comes a new prime.
Quadrapole primes are twin-primes back to back. In the old-Natural
Numbers the closest we came to quadrapole primes was 3,5,7. Now
if 9 were a prime and obviously it is not a prime but if it were a
prime
then 3,5,7, 9 would be a quadrapole prime and I just did this so as
the reader can better understand the situation. In Infinite Integers
the Natural-Numbers have infinitude of Quadrapole Primes and using
pi transposed for rootstock these would be quadrapole primes:
..........56295141307
..........56295141309
..........56295141311
..........56295141313
Now obviously I cannot use any infinite integer that ends in "5" since
it is divisible by 5. And using the same technique as Twin Primes,
these quadrapole primes are infinite.
And using pi as rootstock and quadrapole primes I can continue the
series above skipping "15" as not prime but then starting with 17
ending
to next with a 19 ending with next a 21 ending to next a 23 ending can
can produce the most dense sequence of primes in all the Natural
Numbers.
Proof of the Infinitude of 4-primes, 6-primes, 8-primes etc etc:
I used to call them the quad primes and hex primes and octo primes and
deca primes etc etc. But they are all the even spaced metric primes
and
that twin primes are just a minor category of these even spaced
primes.
The proof of this theorem of the more generalized twin primes follows
the same technique as above for Twin Primes. Only instead of a spacing
of 2 metric units apart they are of a different even number apart. For
example the 4-primes I use the pi rootstock and construct 4 metric
units apart.
..........56295141307
..........56295141311
And now by moving up the string (leftwards) and changing the "3" to
that
of a 4 and then changing the "1" to that of a 2 and continuing to
change
a digit does not affect the fact of irrationality and thus it
maintains its
primeness. And thus I have constructed and infinite set of these even
spaced 4-primes. The same construction for 6-primes, 8-primes etc etc
Now many people if they opened the book to this chapter without
reading the preceding chapters would say these proofs are not what
the old Twin Primes were and that twin primes was meant to be proven
by what we think of as the old Natural Numbers. And my answer to them
is that the old Natural-Numbers never existed in the first place just
as
fire-breathing dragons never
existed and that a physicist would never waste time on injecting fire
breathing
dragons into the study of physics.
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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