Goldbach-Twin conjecture

Let $\mathcal{P}$ be the set of prime numbers, and let a twin prime mean a prime belonging to a pair of primes differing by $2$. For a positive even natural number $n$, consider representations of the form

$$m=p+q.$$

Goldbach-Twin conjecture. For any positive even natural number $n$, there are at least two prime numbers $p,q\in\mathcal{P}$ such that $m=p+q$ and $p$ or $q$ is a twin prime. The statement appears in the source as a proposed combination of Goldbach's conjecture with twin primes. The variable $m$ is used in the assertion although the quantifier names $n$; the supplied text gives no resolution evidence.