Sophie Germain prime
A sequence ("p", 2"p" + 1, 2(2"p" + 1) + 1, ...) in which all of the numbers are prime is called a Cunningham chain of the first kind. Every term of such a sequence except the last is a Sophie Germain prime, and every term except the first is a safe prime. Extending the conjecture that there exist infinitely many Sophie Germain primes, it has also been conjectured that arbitrarily long Cunningham chains exist, although infinite chains are known to be impossible.