Cunningham chain of the first kind
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Contents
Definition
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.
Testing/listing
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 .
