The second answer to this question says the following:
"I believe that sieve methods (in particular methods similar to Chen's result on "almost" Goldbach and twin primes) should give infinitely primes $p$ such that $\frac{p-1}{2}$ is a product of two primes".
Is this claim indeed true and why?
Notice that by Dirichlet's theorem we can obtain the following claim: Given two arbitrary primes $Q$ and $R$, there are infinitely many primes $p$ of the form $1+2nQR$, then $\frac{p-1}{2}=nQR$, so the given product of the two primes, $QR$, divides $\frac{p-1}{2}$.
Thank you very much!