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.
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Peter
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2FYI, using an Approach0 search, there's For $n\ge4,$ prove that $F_n+1$ is not prime, where $F_n$ is $n^{th}$ Fibonacci number., where Sil's answer gives a more general solution, with it referencing an AoPS thread's post containing a proof confirming there is no such prime $p \gt 7$. – John Omielan Jun 15 '23 at 19:31