Suppose p$p$ is a twin prime such that (p, p + 2)$p + 2$ is also prime, and nothing else is known about p$p$.
Is there any reason to think that this affects the probability that p$p$ is also a Sophie Germain prime? Other than the fact that p mod 6$p \pmod 6$ would have to be 5$5$? It would seem that the answer has to be no, but I have some perplexing computational results that I would like to account for.
