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"We can therefore make a further conjecture in the simplest case every sum of two primes, less 2, is the sum of two composites. "
this is already not true though. You just used an example of u + v + 2 = 4, which is only possible for "u" and "v" being "1". but 1 is not a composite number
The smallest odd composite is 9... so the smallest possible example using composites would be 18, which is in fact a sum of primes 7 and 11
"And every odd number greater than 1 is the sum of an odd number and an even number"
this is another mistake. the example even number "2" is a sum of two odd numbers "1" and "1" only... this only applies to odd numbers greater than 2 -
""We can therefore make a further conjecture in the simplest case every sum of two primes, less 2, is the sum of two composites. "
this is already not true though. You just used an example of u + v + 2 = 4, which is only possible for "u" and "v" being "1". but 1 is not a composite number"
Thats the whole point.
If the new conjecture is false, by definition goldbach must be false. -
also:
"We can therefore make a further conjecture in the simplest case every sum of two primes, less 2, is the sum of two composites. "
since a "composite number" is defined as "a positive integer that can be formed by _multiplying_ two smaller positive integers", in the best case, you're just confusing terminology. -
@Wisecrack no no, your statement is false because your whole premise is false to begin with.
You didn't disprove goldbach, you made up your own maths by accident :D
Look, since 1 is not a composite number, as you claim, then you can't claim that every even number is the sum of two composites plus 2.
In fact the example 2+2=4 disproves your own claim immediatelly -
Wherein I disprove Goldbachs Conjecture (in one specific case)
golbach conjecture:
every even number is the sum of two primes
lets call the primes p and q
lets call our even number p+q=n
we can go further by establishing two additional variables
u=p-1, v=q-1
therefore every even number is the sum of u+v+2, according to goldbach's own reasoning.
in the simplest case...
p=2, q=2, p+q=4
u=1, v=1, u+v+2 = 4
We can therefore make a further conjecture in the simplest case every sum of two primes, less 2, is the sum of two composites. This likely has connections to the abc conjecture for a variety of reasons. But leaving ancillary discussion aside for a moment...
We can generalize to a statement that every even number is the sum of two odd numbers. And every odd number greater than 1 is the sum of an odd number and an even number.
Finding an even number that is not the sum of (p-1)+(q-1) would therefore be equivalent to disproving the goldbach conjecture. Likewise proving every even number is the sum of (p-1)+(q-1) would be the equivalent of proving it.
Proving all even numbers greater than 2 are the sum of two composites + 2 would be proof of goldbachs conjecture, and finding any example or an equation that proves an example exists such that *some* subset of even numbers are NOT the sum of two composites +2, would disprove the conjecture.
Lets start with a simple example:
2+2=4
because 4-2=2, and two is not the sum of two composite numbers goldbachs conjecture must ipso facto be false.
QED
If I've wildly misapprehended the math, please, somebody who is better at it, correct me.
Honestly if this is actually anything, I'd be floored to discover no one has stumbled on this line of reasoning before.
rant
genius or just retarded