Definition:Cunningham Chain/Second Kind

Definition
A Cunningham chain of the second kind is a (finite) sequence $\tuple {p_1, p_2, \ldots, p_n}$ such that:


 * $(1): \quad \forall i \in \set {1, 2, \ldots, n - 1}: p_{i + 1} = 2 p_i - 1$
 * $(2): \quad p_i$ is prime for all $i \in \set {1, 2, \ldots, n - 1}$
 * $(3): \quad n$ is not prime such that $2 n - 1 = p_1$
 * $(4): \quad 2 p_n - 1$ is not prime.

Also see

 * Definition:Cunningham Chain of the First Kind