It's a well-known open problem (Sophie-Germain primes) whether there are infinitely many primes $p$, $2p+1$. What about $p$, $2p-1$?


Seemingly it's also an open problem (see [here](https://math.stackexchange.com/questions/1472622/pair-of-primes-of-the-form-4k3-and-8k5) and the linked question). 
I am aware that it is a special case of more general open problems. 


But I'd like a concrete reference asserting that this specific problem is indeed open.


Edit: As I said, I'm not interested in more general conjectures. It's suitable for MO, because no one has given me a reference for this exact problem.



Primes $p$ for which $2p-1$ is prime
I agree with Felipe Voloch that this question is not quite suitable for MO. At any rate, it is well-known (folklore) among number theorists that solving any single $k=2$ case of [Dickson's conjecture](https://en.wikipedia.org/wiki/Dickson's_conjecture) would be a major breakthrough. The best approximations we know are in the works of Green-Tao, Zhang-Maynard-Tao-Polymath (and studying these works makes one understand why any single $k=2$ case is hard).


