— Burt Kaliski Jr. (@modulomathy) September 11, 2013
A Sophie Germain prime is a prime p with the property that 2p+1 is also prime. The prime q = 2p+1 is called the matching safe prime, because of its advantages in cryptographic applications against certain attacks (in particular those based on the value q-1 having too many small prime factors – which can be avoided here simply by ensuring that p is large enough, so that the only small prime factor is 2).
The prime factors of 253 and 11 and 23. The first factor is the Sophie Germain prime and the second factor is the matching safe prime.