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From: Archimedes Plutonium on 12 Aug 2010 04:59


Archimedes Plutonium wrote:
> 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.
>

Sorry about all that thrashing around, but am settled, although tired.
It is not a proof by
Mathematical Induction nor Fermat's Infinite Descent, although it
appears as such.

I figured out what makes it work, or what forces it to become a
summand of two primes.

It is not by contradiction.

Let me use the example of 100 again and pretend as if at 100, the
Goldbach breaks down
and has no two prime summands. So I haul in the Goldbach Universal
Repair Kit. It is very simple kit and looks like this (K-2, 2) and the
K is 100 where Goldbach broke down, so I
drop down to the previous Goldbach that worked-- 98. So the (K-2, 2)
is (98,2)

Now I look for all the primes that satisfy Goldbach at 98 and they are
(67,31) and (37, 61)
and (79,19).

Now how does the Goldbach Repair Kit become so Universal in fixing any
even number that
is broken down with only one prime summand? It is easy to see how it
is Universal, for watch how it repairs 100.

I take 67 and 31 and immediately try adding 2 to either one to see if
I can end up with two
prime summands, and nope, it does not work. So now I play the second
round trick and add 4
to one while subracting 2 from the other to see if I can come up with
two prime summands? And the answer is yes for I can get (29,71).

But let me continue with round three where I add 6 and subtract 4 from
one to the other. With the summands of (67,31) how many rounds can I
play with adding and subtracting? Well I can
play this rounds to the limit of subtracting 28 and adding 30.

And what forces it to always work and repair the damaged Goldbach even
number? It is easy to see why it must work universally. If it did not
work means there are no primes in the interval 0 to 100 that are
separated by a metric length of 2, by a length of 4, of 6 of 8 of 10
all the way to 50.

As I wrote the first twenty five primes above:
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

The primes 3 and 97 are of length 94, the primes 5 and 97 are of
length 92 etc etc.

If Goldbach was false at 100, means there are no prime pairs between 0
and 100 of lengths
30 to 60.

So we see why Goldbach has to be true, otherwise we would have the
primes from 0 to
100 be only this set: 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97

So here I have given a proof of Goldbach without the referral to the
Algebra that every Even
Natural >2 has at minimum two prime factors. The above Proof works
because the repair kit is universal, and it must work for the reason
that there are no large holes in the primes given a metric length. So
there is something new in mathematics in this proof. The idea of a
repair kit has never been used before.

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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