# Bitwin chain

## Definition

A bitwin chain of length  is defined as a collection of natural numbers:



such that all the numbers in the chain are prime.

Note that the numbers  forms a Cunningham chain of the first kind of length , while  forms a Cunningham chain of the second kind. Each of the pairs  is a pair of twin primes. Each of the primes  for  is a Sophie Germain prime and each of the primes  for  is a safe prime.