若质数为索菲热尔曼质数，则亦为质数。索菲·热尔曼证明了费马最后定理对于这类质数为真。且若均为整数，在这式子内，必有一项能被整除。

是否存在无限个索菲热尔曼质数仍属猜想。

从1到10000共有190个索菲热尔曼质数（OEIS中的数列A005384）：

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 29 is a Sophie Germain prime and 2 × 29 + 1 = 59 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem. Sophie Germain primes and safe primes have applications in public key cryptography and primality testing. It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven.