Similar to Goldbach Conjecture I have thought of a conjecture similar to Goldbach Conjecture. I have shown the result to be true with a program in C++ up until $n=30000$.

$\forall n>2$ with $n$ even,there exists two primes $p,q$ with $n<p,q<2n$ $\;$ and $\;$  $p+q=3n$

We know Betrand's postulate:

For any integer $n > 3$, there always exists at least one prime number $p$ with
  $n < p < 2n - 2$.

But I don't know if this postulate can help me.
I wanted to place it somewhere public so people can think about it.
Are there any results similar to this?

There are various known modifications of the Golbach conjecture were restrictions are imposed on the size of the summands. 
This idea is not really original. 
Bertrand's postulate is a very weak result; it is extremely unlikley to be of direct use in the proof of a conjecture that should be rather more difficult than the Goldbach conjecture.  
