Is this a known conjecture? Given odd primes $p,q$ with $p + q$ sufficiently large, must there exist a different pair $p',q'$ with $p+q = p'+q'$? Conjecture:

There is a natural number $N\in\mathbb N$ such that given odd primes $p,q$ with $p+q>N$
  there are primes $p',q'$ where $p' \notin \{p,q\}$ such that $p+q=p'+q'$.

Is this known?

Restricted to odd primes, the conjecture is that the number of Goldbach partitions is 0 or at least 2, with finitely many exceptions.  The Goldbach conjecture is  that this number is never 0.
See also Goldbach's comet.

Not restricted to odd primes, as lulu points out in the comments, the conjecture is false.
