Symmetric prime pairs around $m$ for $m > 2\cdot 10^{18}$

For every natural number $m > 2\cdot 10^{18}$ there exists $t \le m - 2$ such that both $m - t$ and $m + t$ are prime.

This is the symmetric form of the even Goldbach conjecture: writing $2m = (m - t) + (m + t)$ shows that it is exactly equivalent to the claim that every even $n > 4\cdot 10^{18}$ is a sum of two primes. It is the formulation targeted by symmetric-window approaches to the conjecture.