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From: Archimedes Plutonium on 13 Aug 2010 01:59

It may not be obvious to some viewers that I have not yet achieved a
proof of Goldbach.
Sometimes in excitement I overstate things. Goldbach is not yet here,
proven. It would be
proven if I had a Galois Algebra that could mirror image
multiplication with addition since
in multiplication, every Even Integer >2 requires a decomposition into
at minimum two prime
factors. So if multiplication were interchangeable with addition,
Goldbach would instantly be
proven true. It reminds me of the proofs in Projective Geometry where
theorems on lines are
interchangeable with the same theorems by translation into points. So
can we substitute lines for multiplication and points for addition and
do a Projective Geometry proof of Goldbach? Perhaps mathematics in the
22nd century will be trespassing into this new arena of mathematics.

But here I am trying to make a conventional proof out of Goldbach, if
that is possible, or like
Fermat's Last Theorem or the Riemann Hypothesis, perhaps, Goldbach is
amongst those that
can only be proven up to 10^500 and hence true. And that no
conventional proof is able because Goldbach has counterexamples in the
AP-adics Infinite Integers.

The good news so far, is that I truly do have proofs of Infinitude of
Twin Primes, Polignac, Mersenne Primes, Infinitude of Perfect Numbers
and a proof that No Odd Perfect Numbers,
other than 1 Exist.

It is just that Goldbach is hung up.

What I need to make the above a conventional proof is a theorem that
says something along these lines of the Goldbach Repair Kit. Let us
say I am given an Even Integer like 100 and
let me suppose that Goldbach breaks down at 100, then 98 is the last
time that Goldbach was
still good and that 98 has (61,37) as Goldbach summands. What I need
as a theorem to
prove Goldbach is that by a recursive manipulation of 61 and 37

(61,37) with adding 2 to find two new prime summand pair
(61,37) with adding 4 but subtracting 2 to find two new prime summand
pair
(61,37) with adding 6 but subtracting 4 to find two new prime summand
pair
ad infinitum

If there is a theorem that can be proven that given any Goldbach
summand pair for Even
Integers >6 that the process above always insures a new two prime
summand pair.

So I have reduced the Goldbach Conjecture to a theorem that says
basically every Even
Integer >6 has a new prime summand pair out of the Repair Kit (K-2,2)

Now in the 1990s I was using the Chebychev theorem that between M and
2M always exists a prime, but I do not think Chebychev theorem is
applicable here. The above has more of a
hint to Polignac of primes spaced apart by a 2k metric.

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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