Cunningham chain of the first kind

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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

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 .