A non-Chen prime is a prime $p$ such that $p+2$ is neither a prime nor a semi-prime. $3^6+3=732$ is divisibile by the non-Chen prime $61$. On the other hand, $2^6-3=61$.
Are there infinitely many $k$ such that both $3^k+3$ and $2^k-3$ are divisibile by the same non-Chen prime? Could somebody find another example besides $k=6$ ?