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From: Ludovicus on 14 Jun 2010 19:20
On Jun 14, 11:12 am, raycb <ra...(a)live.com> wrote:

> After I made that first post, I had doubts about saying that it was
> equivalent to the Goldbach conjecture. I withdraw it.
>
> I wasn't intending to say -- this is true -- I dare you to prove me
> wrong. I was saying -- this is most very likely false -- where does
> the first counterexample appear?
>
> From a small number of observations I found that the even numbers
> above 6 could be written as the sum of two primes in a way that at
> least one of the primes was six less than another prime. The
> conjecture is that this pattern continues without end.

There is not any mystery that by summing 6 to one of the two primes of
a Goldbach
decomposition one obtain another prime, because the proportion of
primes
of the form: prime + 6 is enormous .
Example: Between 1000000 and 1100000 there are 7180 primes, 1130
having
a difference of 6.
Ludovicus
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