# Definition:Safe Prime

## Safe Prime

A safe prime is a prime number $p$ of the form:

$p = 2 q + 1$

where $q$ is also a prime number.

It follows from this definition that $q$ is a Sophie Germain prime.

### Sequence of Safe Primes

The sequence of safe primes begins:

$5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, \ldots$