Re: Who thinks Goldbach's Conjecture is unprovable?

From: Luis A. Rodriguez (luiroto_at_yahoo.com)
Date: 10/06/04 

Date: 6 Oct 2004 09:51:26 -0700

luiroto@yahoo.com (Luis A. Rodriguez) wrote in message news:<c9ba0a0b.0410041107.3d27929f@posting.google.com>...
> >. But the only reason you've given for *suspecting*
> > unprovability is the fact that it's been on the table awhile and
> > is not yet proven. Do you suspect unprovability of every old
> > unsolved problem? If not, then why GC particularly?
> >> Todd Trimble
>
> No, the suspect of the unprovability of Goldbach Conjecture is based
> in solid arguments related to the "random" or chaotic behavior of
> prime numbers. FLT was a different problem, because from the begining
> it was related to algebraic aspects of numbers.
> Here is a probabilistic presentation of the difficulties of G.C.
> Suppose I want to know what are the solution of the problem p1+p2 = 68.
> The maximum possible values of p1 and p2 are: p1 = 2n-1 ; p2 = 2n+1
> 4n = 68 ---> n = 17
> In the inferior row are the odd integers from 3 to 2n + 1.
> In the left column are the odd integers from 2n -1 to 4n - 3.
>
> 33 N
> 35 N
> 37 Y
> 39 N
> 41 N
> 43 N
> 45 N
> 47 N
> 49 N
> 51 N
> 53 N
> 55 N
> 57 N
> 59 N
> 61 Y
> 63 N
> 65 N
> 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
>
> When the number of the row is a prime AND also the number of the colummn,
> we have a Y that means that we found a solution of p1 + p2 = 68
> What if this two solutions,and the others, are a fortuitous event resulting from the density of the primes and its chaotic distribution?

The number of decompositions of a large even number as the sum of two
primes
can be calculated, with great aproximation, with a formula deducted
from probabilistic considerations based in the preceding diagram. If N
is the even number, the number of decompositions is aprox. = N /
[Log(N)*(Log(N/2) - 1)]

Moreover, Rodriguez and Bowker verified that the primes are too
numerous, that is, with less than half of the actual primes, GC is
fulfiled. Ex. 13 are sufficient for the even numbers < 100 and 51 are
sufficient for the even<1000.
Bowker advanced the conjecture that SQR(N)*LOG(LOG(N))primes are
sufficient.

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