Category:Definitions/Cunningham Chains
Jump to navigation
Jump to search
This category contains definitions related to Cunningham Chains.
Related results can be found in Category:Cunningham Chains.
There are $2$ types of Cunningham chain:
First Kind
A Cunningham chain of the first kind is a (finite) sequence $\tuple {p_1, p_2, \ldots, p_n}$ such that:
- $(1): \quad \forall i \in \set {1, 2, \ldots, n - 1}: p_{i + 1} = 2 p_i + 1$
- $(2): \quad p_i$ is prime for all $i \in \set {1, 2, \ldots, n - 1}$
- $(3): \quad n$ is not prime such that $2 n + 1 = p_1$
- $(4): \quad 2 p_n + 1$ is not prime.
Thus:
- each term except the last is a Sophie Germain prime
- each term except the first is a safe prime.
Second Kind
A Cunningham chain of the second kind is a (finite) sequence $\tuple {p_1, p_2, \ldots, p_n}$ such that:
Pages in category "Definitions/Cunningham Chains"
The following 5 pages are in this category, out of 5 total.