Are there infinitely many primes $p_k$ such that $(p_k-1)!+p_k$ is a also prime?

Question

I am wondering whether there are infinitely many primes $p_k$ such that $(p_k-1)!+p_k$ is also prime. Given that $p_k \equiv 2 \pmod 3$.

For a very large prime, I can assume Stirling's approximation. But it doesn't say anything about factorization or Primality of the number.