0
$\begingroup$

Goldbach's conjecture states that every even integer greater than $2$ is the sum of two (not necessarily distinct) prime numbers.

It seems that for $n>6$ , we can choose a representation with distinct primes. This leads to the following lighter conjecture :

Let $p>3$ be a prime number , then there are distinct primes $q$ and $r$ with $2p=q+r$

Is this conjecture as difficult as Goldbach itself , or is a proof known ?

I guess this has been verified upto the same limit as Goldbach. The lighter conjecture holds for $p\le 10^9$

$\endgroup$
1
  • $\begingroup$ I guess it is no simpler than Goldbach itself. $\endgroup$ Jun 14, 2023 at 11:28

1 Answer 1

0
$\begingroup$

To me they are equally hard, since I can’t prove either. But consider this: Someone doesn’t proof Goldbach directly, but proves there are at least x solutions with not necessarily distinct primes, and then proves x > 1.7. This would prove Goldbach, but not your conjecture.

On the other hand, someone might prove an upper bound for the number of Goldbach counterexamples, which isn’t good enough for a proof of Goldbach. But turns out to be good enough for your conjecture, because you only examine n/log n numbers.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .