Let's consider the example,
$$ 3 + 11 + 19 = 33 \\ 2 + 31 = 33 $$
we can see that there are cases where the sum of 3 primes be expressed as the sum of 2 primes. However, I couldn't find a case where a sum of 3 primes couldn't be expressed as a sum of 2 primes.
Is there such a conjecture already in the world of mathematics? Or is there a counter example?