Cunningham chain

In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes.

A Cunningham chain of the first kind of length n is a sequence of prime numbers (p₁, ..., p_n) such that for all 1 ≤ i < n, p_i+1 = 2p_i + 1. (Hence each term of such a chain except the last one is a Sophie Germain prime, and each term except the first is a safe prime).

It follows that

Or, by setting ${\displaystyle a={\frac {p_{1}+1}{2}}}$ (the number ${\displaystyle a}$ is not part of the sequence and need not be a prime number), we have ${\displaystyle p_{i}=2^{i}a-1}$

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