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From: Archimedes Plutonium on 12 Aug 2010 11:34

Amazing what difference sleep makes and doing mathematical proofs.

By all means it was a Fermat's Infinite Descent Mathematical Induction
Proof starting with 8.

Here is how it goes.

Universal Goldbach Repair Kit, like in a auto racecourse they repair a
flat tire by removing the
whole tire.

Starting with 8 we have (K-2, 2) so we have (6,2) where 2 is a singlet
prime in a Goldbach summand and we require two primes for the summand.
The number 6 obeyed Goldbach with
(3,3) and now we have increments of 2 to fix and repair 8. So we can
either add 2 or add 4 and subtract 2, or add 6 and subtract 4, etc etc
to the two summands of the K-2. For 8 we have
3+2 =5 so we have (5,3) and done. For 10 we have (K-2,2) is (8,2)
which gives us ((5,3),2)
and with the adding of 2 to 3 we end up with (5,5). So the initial-
induction-step is set with
8 and 10.

Now we assume the general case (K-2,2) and by Fermat's Infinite
Descent we end up coming back and saying that if the general case
fails, then it ends up that it fails for 10 and finally 8.
The reason we can say this is because, as explained, the adding and
subtracting in increments of 2, this recursive procedure:

add 2
add 4, subtract 2
add 6, subtract 4
add 8 subtract 6

That procedure causes the generalized case (K-2,2) to force the
nonexistence of
10 and finally 8 as not the summands of two primes.

I do not know if anything at all is new in this proof of Goldbach,
whether a Repair Kit
like that was ever used in a mathematical proof is an open question to
me.

I still am going to pursue the Algebra proof for it is far more
splashier and full of pizzazz.

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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