What is the conjecture

https://www.erdosproblems.com/1072

For any prime $p$, let $f(p)$ be the least integer such that $f(p)!+1\equiv 0\pmod{p}$.

Is it true that there are infinitely many $p$ for which $f(p)=p-1$?
Is it true that $f(p)/p\to 0$ for almost all $p$?

Status: open

Choose either option

• I plan on working on this conjecture
• This issue is up for grabs: I would like to see this conjecture added by somebody else