Erdős problem 1074

Similarly, if $P$ is the set of all primes $p$ such that there exists an $m$ with $p\not\equiv 1\pmod{m}$ such that $m! + 1 \equiv 0\pmod{p}$, then does $$\lim\frac{|P\cap[1, x]|}{\pi(x)}$$ exist?