Is it known whether $6\times 10^n\pm 1$ is a twin prime for some $n>2$?

Question

I checked the number pairs $6 \times 10^n \pm 1$ for $1 \le n \le 2000$.

The only twin primes of the desired form I found are: $(59, 61)$ and $(599, 601)$.

I wonder if these are the only pairs.

What is the smallest twin prime of the form $6 \times 10^n \pm 1$ with $n > 2$ ?

Answer 1

OEIS has sequences A056716 (-1) and A056805 (+1) and there is no other intersection up to $n=500000$.