安全素数是满足2p＋1形式的一类数，在这里p也是素数。（相反地，素数p叫做索菲热尔曼素数。）开始的几个安全素数是：

A safe prime is a prime number of the form 2p + 1, where p is also a prime. (Conversely, the prime p is a Sophie Germain prime.) The first few safe primes are

With the exception of 7, a safe prime q is of the form 6k − 1 or, equivalently, q ≡ 5 (mod 6) — as is p > 3 (c.f. Sophie Germain prime, second paragraph). Similarly, with the exception of 5, a safe prime q is of the form 4k − 1 or, equivalently, q ≡ 3 (mod 4) — trivially true since (q − 1) / 2 must evaluate to an odd natural number. Combining both forms using lcm(6,4) we determine that a safe prime q > 7 also must be of the form 12k−1 or, equivalently, q ≡ 11 (mod 12).