Is there a prime $p>7$ of the form $F_n\pm 1$?

Question

Let $F_n$ be the $n$-th fibonacci number.

For $n\le 60\ 000$ , the largest prime of the form $F_n-1$ or $F_n+1$ is $7=F_6-1$

Is there another prime of one of the forms ?

It must have more than $12\ 000$ digits.