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From: Archimedes Plutonium on 12 Aug 2010 01:26
I have the proof, yes indeed, and it does not need any algebra. It
simply is a Fermat Infinite
Descent or mathematical induction. It is rather a pathetically silly
proof in that it does not
teach us anything new and the technique of mathematical induction is
rather boring and not
stimulating. So I rather wish we can find the Galois Algebra of
interchange between addition and multiplication to liven up the
Goldbach proof.

I will not formally write the proof but just give the outline. The
idea of the proof is that at some
juncture of the Even Naturals we suppose hypothetically that Goldbach
fails and call this number K. It has only a singlet prime summand and
we call it 2 so the pair is (K-2, 2)

Now we dissect K-2 for it does obey Goldbach and it has two prime
summands of p_1 and
p_2 and we add 2 to either p_1 or p_2 in hopes of repairing K so that
both summands are now
two primes. If not, then we go to (K-3, 3) and do the same procedure,
and if that does not work
we go to (K-5, 5). Eventually in this process we end up with two prime
summands and the contradiction that accrues is that 4 does not equal
2+2 or that 6 does not equal 3+3.

Or, possibly the Polignac Conjecture proved recently is the
contradiction.

Classic Fermat Infinite Descent. So rather disappointed in the lack of
pizzazz. Would rather
explore a Algebra interchange or Projective Geometry Interchange with
multiplication and addition.

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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