Germain primes

A prime p is said to be a Sophie Germain prime if both p and 2p + 1 are prime. The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, ... (OEIS A005384). It is not known if there are an infinite number of Sophie Germain primes. The numbers of Sophie Germain primes less than 10^n for n = 1, 2, ... are 3, 10, 37, 190, 1171, 7746, 56032, ... (OEIS A092816). The largest known proven Sophie Germain prime pair as of Feb. 29, 2016 is given by (p, 2p + 1) where p = 2618163402417·2^1290000 - 1 (Caldwell), each of which has 388342 decimal digits (PrimeGrid).

Cunningham chain | Fermat's last theorem | Mersenne number | twin primes