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From: Archimedes Plutonium on 12 Aug 2010 02:37

Let me throw out the last post, as a too tired to think properly with
the mistakes of
(K-3, 3) , (K-5, 5) for those are not even numbers. Let me start over
to see if (K-2,2)
can by itself handle all Goldbach repairs.

Here are the first twenty five primes:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97

Now let me go through all the even numbers from 8 to 100 and see if
the (K-2,2) repair kit
works all all those even numbers.

For 8 we have (6,2) which decomposes to ((3,3), 2) and generates
(3,5). So it works with 8

For 10 we have (8,2) which decomposes to ((5,3),2) and generates
(5,5). So it works with 10

Let me skip to 100 and work downwards

For 100 we have (98,2) which decomposes to ((79,19),2) and generates
nada, but however I
notice that if I subtract 2 from 19 and add 4 to 79 yields (83,17)

So I think I may have a universal repair kit for Goldbach where I can
always add 2 or subtract 2 but add 4 to the other, or subtract 4 and
add 6 to the other.

So I think the Fermat Descent or Mathematical Induction works with
this universal repair kit of
Goldbach and it always starts with a (K-2, 2) and then it tinkers with
the two primes in the K-2
kit adding or subtracting even numbers.

It would thus not be a proof by contradiction but directly from
Mathematical Induction.

Again, though, let me repeat, the above has no pizzazz, and so will
try to turn it into a Projective Geometry of point versus line as
multiplication versus 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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