Let $\ p\ $ and $\ q:=2\cdot p+1\ $ be primes — they are called Germain prime siblings. Such a pair belongs to the first type $\ \Leftarrow:\Rightarrow\ q^2\equiv\pm1\mod8,\ $ and to the second type $\ \Leftarrow:\Rightarrow\ q^2\equiv\pm3\mod8.\ $

Do you know any results (in print or your own) about the frequency of the two types?

Let $\ p\ $ and $\ q:=2\cdot p+1\ $ be primes — they are called Germain prime siblings. Such a pair belongs to the first type $\ \Leftarrow:\Rightarrow\ \frac{q^2-1}8\equiv\pm1\mod8,\ $ and to the second type $\ \Leftarrow:\Rightarrow\ \frac{q^2-1}8\equiv\pm3\mod8.\ $

Do you know any results (in print or your own) about the frequency of the two types?