So I know that if both $p$ and $2p + 1$ are primes, then $p$ is a Sophie Germain prime from the Prime Glossary.

My question is this: How do we call a prime $r=(q+1)/2$ such that $q=2r-1$ is also prime?

I searched for the first $6$ terms via OEIS and I got sequence A005383:

$$3, 5, 13, 37, 61, 73, \ldots$$

However, there does not seem to be any explicit mention of a specific terminology for such primes $r=(q+1)/2$ in the literature and on the Internet.

Does anybody here know of an existing terminology for such primes $r$?


  • 2
    $\begingroup$ If it doesn't have a special name on OEIS then it probably doesn't have one at all. $\endgroup$ – man and laptop May 22 '15 at 16:52

$r$ is the base of a Cunningham chain of the second kind. A Sophie-Germain prime is the base of a Cunningham chain of the first kind.


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