Infinitely many primes $p$ such that $\frac{p-1}{2}$ is prime

Question

After asking this question and receiving interesting comments, the following, seemingly easier, question arises:

Are there infinitely many primes $p$ such that $\frac{p-1}{2}$ is a prime number?

Examples for $(p,\frac{p-1}{2})$: $(5,2),(7,3),(11,5),(23,11)$.

Remark: Unfortunately, I did not understand the claims in the comments of the above mentioned question, so perhaps my current question has a positive answer by those comments (please see my last comment there, in which I ask if Lemma 1 of https://academic.oup.com/qjmath/article-abstract/37/1/27/1515517?redirectedFrom=PDF answers my current question).

Edit: After reading the answer below, I guess that "seemingly easier" should be deleted.

Thank you very much!

Answer 1

A positive answer to this question would imply that there are infinitely many Sophie Germain primes, but this is not known.