Cunningham chain of the first kind
Let be a natural number. A Cunningham chain of the first kind of length is a sequence of primes such that for each .
A complete Cunningham chain of the first kind is a Cunningham chain of the first kind that cannot be extended further in either direction.
Given a Cunningham chain of the first kind of length , the first prime in the chain is a Sophie Germain prime and the second prime in the chain is a safe prime. More generally, in any Cunningham chain of length , the first primes are Sophie Germain primes and the last primes are safe primes.
Related facts and conjectures
Relation with other properties
- Cunningham chain of the second kind
- Bitwin chain is a combination of Cunningham chains of both kinds and twin primes.
The ID of the sequence in the Online Encyclopedia of Integer Sequences is A005602
This lists, for every , the smallest prime beginning a complete Cunningham chain of length .