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From: Archimedes Plutonium on 17 Jul 2010 04:20
--- quoting from Wikipedia on some other unsolved prime number
problems ---
Other conjectures relate the additive aspects of numbers with prime
numbers: Goldbach's conjecture asserts that every even integer greater
than 2 can be written as a sum of two primes, while the weak version
states that every odd integer greater than 5 can be written as a sum
of three primes.
--- end quoting ---

Alright, I already proved the stronger form of Goldbach Conjecture: to
summarize that proof:
We simply note that in multiplication there is Unique Prime
Factorization of each number
and that the even numbers such as 8 are decomposed into 2x2x2. So in
multiplication, 8
has three prime factors, but in addition 8 has two primes of 3+5. So
the proof of Goldbach
is a very strong, zugswang proof, I mean I literally have a
stranglehold on the throat of the
Goldbach Conjecture. The proof is that every even number in
multiplication must have at least
two prime factors, for it must have a 2, and then it must have some
other prime factor, but always at least two. Now, for the final step.
We know that Galois Algebra theory makes no distinction between add or
multiply. Either operator exists for the Group, Ring, Field. They are
interchangeable, just as the line is interchangeable with point in
Projective Geometry. Call it
the Interchangeable Principle or call it the Galois Algebra Principle.
Or it may have a name already which I am not aware of. But the fact
is, in mathematics, in Algebra, addition is interchangeable with
multiplication, and if it is required at a minimum for multiplication
that an
even number must always have at least two prime factors, then we
switch over to addition
and thus each even number must have two primes that add up to that
even number.

Now the proof of the weaker version of Goldbach that every odd number
beyond 5 has three
prime addends.

Proof: given any odd number larger than 5, suppose for clarity we are
given 19. Then we know
from the proof of Goldbach strong version, that 18 has two prime
addends and that 16 has two
prime addends. Since 16 has two prime addends we simply join the prime
number "3" to the
addends of 16. So whatever odd number larger than 5, we simply use the
prime "3" and join it with the even number of 3 units away, thus every
odd number larger than 5 has three prime addends.

The important feature of Goldbach is that it forces us to explore in
depth this greater idea that
multiplication and addition are interchangeable as is point with line
in Projective Geometry.


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
From: christian.bau on 17 Jul 2010 04:51
On Jul 17, 9:20 am, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> --- quoting from Wikipedia on some other unsolved prime number
> problems ---
> Other conjectures relate the additive aspects of numbers with prime
> numbers: Goldbach's conjecture asserts that every even integer greater
> than 2 can be written as a sum of two primes, while the weak version
> states that every odd integer greater than 5 can be written as a sum
> of three primes.
> --- end quoting ---
>
> Alright, I already proved the stronger form of Goldbach Conjecture: to
> summarize that proof:
> We simply note that in multiplication there is Unique Prime
> Factorization of each number
> and that the even numbers such as 8 are decomposed into 2x2x2. So in
> multiplication, 8
> has three prime factors, but in addition 8 has two primes of 3+5. So
> the proof of Goldbach
> is a very strong, zugswang proof, I mean I literally have a
> stranglehold on the throat of the
> Goldbach Conjecture. The proof is that every even number in
> multiplication must have at least
> two prime factors, for it must have a 2, and then it must have some
> other prime factor, but always at least two. Now, for the final step.
> We know that Galois Algebra theory makes no distinction between add or
> multiply. Either operator exists for the Group, Ring, Field. They are
> interchangeable, just as the line is interchangeable with point in
> Projective Geometry. Call it
> the Interchangeable Principle or call it the Galois Algebra Principle.
> Or it may have a name already which I am not aware of. But the fact
> is, in mathematics, in Algebra, addition is interchangeable with
> multiplication, and if it is required at a minimum for multiplication
> that an
> even number must always have at least two prime factors, then we
> switch over to addition
> and thus each even number must have two primes that add up to that
> even number.
>
> Now the proof of the weaker version of Goldbach that every odd number
> beyond 5 has three
> prime addends.
>
> Proof: given any odd number larger than 5, suppose for clarity we are
> given 19. Then we know
> from the proof of Goldbach strong version, that 18 has two prime
> addends and that 16 has two
> prime addends. Since 16 has two prime addends we simply join the prime
> number "3" to the
> addends of 16. So whatever odd number larger than 5, we simply use the
> prime "3" and join it with the even number of 3 units away, thus every
> odd number larger than 5 has three prime addends.
>
> The important feature of Goldbach is that it forces us to explore in
> depth this greater idea that
> multiplication and addition are interchangeable as is point with line
> in Projective Geometry.
>
> Archimedes Plutoniumhttp://www.iw.net/~a_plutonium/
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies

I have four questions:

1. What is the meaning of "join" in your proof?
2. Which of the two numbers 3 units away do you mean?
3. What makes you think such a trivial proof is worth posting?
4. How can you mess up such a trivial proof?
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