I know the importance of the series of series involving prime numbers or constellations of prime numbers in the analytic theory of numbers. For example, if I am not mistaken, the major theorems are Mertens' theorems or Brun's theorem. On the other hand, I know from an informative point of view that the literature contains other more complicated statements and / or conjectures about the convergence of series with prime numbers, see for example the first paragraph of the section. E7 From 1).
Motivation. I'm just going to ask for the next constellation of numbers with the aim that my question is not too broad, but I think focusing attention on the sequence of strong prime numbers is interesting, see Wikipedia. First fort, because of the applications of this sequence of prime numbers. Also, I would like to know your good intuition / reasoning to get statements or conjectures of this kind.
Question. What can be interesting series involving sequences of strong prime numbers? I speak of statements or conjectures concerning convergent or divergent series involving strong prime numbers. I am talking about series with good mathematical content or meaning in mathematics. Thank you so much.
I do not know if some series involving such strong prime numbers are in the literature. If this question is welcome, do not hesitate to add the reference. I'm trying to find and read the results of the literature. If not, add your series of genunines to the prime numbers.
(1) Richard K. Guy, Unresolved Problems of Number Theory, Unresolved Problems of Intuitive Mathematics, Volume I, Second Edition, Springer-Verlag (1994).
(2) I also add that the MarthWolrd Encyclopedia has the article Prime Sums.