Cunningham chain of the second kind

Definition

Let $k$ be a natural number. A Cunningham chain of the first kind of length $k$ is a sequence of primes $q_1<q_2<\dots <q_k$ if $q_{i+1}=2q_i-1$ for each $1\le i\le k-1$.

A complete Cunningham chain of the second kind is a Cunningham chain of the second kind that cannot be extended further in either direction.

Relation with other properties=

• Cunningham chain of the first kind
• Bitwin chain is a combination of Cunningham chains of both kinds as well as twin primes.