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From: Archimedes Plutonium on 12 Aug 2010 13:30
For the life of me, I do not know how I got caught into the middle of
the arena of fighting
of Goldbach Conjecture once again. I guess with a little bit of
slipping and sliding, I find
myself in this fight once again. I do recall trying Math-Induction on
Goldbach circa 1991
and became very disheartened, because of the increasing mess, but I
did not have the
Repair Kit idea in 1991. This is the reason I so much love the Algebra
style of proof where
every Even N >4 has a minimum of two multiplicative prime factors, and
converted to
addition, every Even N>4 is the sum of two prime summands. So the
proof of Goldbach,
algebra wise is simply to state that multiplication versus addition
preserves the two prime
minimum requirement.

But let me look for the easiest Mathematical Induction proof of
Goldbach, for that
Fermat's Infinite Descent maybe too messy.

Let me write down some accounting:

For the case of 14 as where Goldbach fails we have (K-2,2) repair kit
which is (12,2)
We thus have ((7,5),2) which yields:
(7,7) in case of +2
(9,5) in case of +2
(11,3) in case of +4-2
(5,9) in case of +4-2
(13,1) in case of +6-4
(3,11) in case of +6-4
(1,13) in case of +8-6

So the Fermat's Infinite Descent would come zooming back to 8 and 6 as
not obeying
Goldbach. But let me see if a zooming outwards of (K-2,2) is a more
practical and less
mess of a Mathematical Induction and using 14 for the case study since
12 has only (7,5)
as Goldbach primes.

So what about if Goldbach breaks down at 14, then a Mathematical
Induction that 16, then 18,
then 20 ad infinitum cannot be broken down or else we have no prime
pairs separated by a metric length of 2,4,6,8, ad infinitum

So the accounting of 16 looks like this:
We thus have ((7,7),2) and ((11,3),2) which yields:
(7,9) in case of +2
(11,5) in case of +2
(13,3) in case of +2
(11,5) in case of +4-2
(15,1) in case of +4-2
(9,7) in case of +4-2
(13,3) in case of +6-4
(7,9) in case of +6-4
(15,1) in case of +8-6
(5,11) in case of +8-6

And we see that (11,5) and (13,3) satisfy Goldbach for +2 beyond where
Goldbach failed at
14. So the idea here, rather than Fermat's Infinite Descent, is that a
Mathematical Induction that zooms outward from the damaged case of
Goldbach is an easier Mathematical Induction.
Because if this zooming out is false implies there are no more prime
pairs of Goldbach summands separated by a metric length of 2, 4, 6, ad
infinitum.

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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