Are these two sequences known to be infinite : A120628 and A079149 ? Reference request

Question

This is a straightforward question. Are the following two sequences known to be infinite: A079149 and A120628? A reference showing their infinitude would be helpful. We have the following reference for A120628 in the comment section: Crandall and Pomerance page 53 exercise 1.18. Crandall and Pomerance say there cannot be infinitely many such primes which conflicts with what the author is suggesting in the comment for A120628?

Answer 1

The sequence A079149 is infinite. More generally, it is known that for any fixed nonzero integer $h$, there are infinitely many primes $p$ such that $p+h$ has at most two prime factors. This is essentially Chen's theorem. A good introduction to this circle of ideas can be found here, for example. The proof proceeds via sieve methods.

The sequence A126028 is not known to be infinite. These are primes $p$ such that either $2p+1$ or $2p-1$ is a prime. In particular, this sequence contains the Sophie Germain primes.