# Definition:Safe Prime

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## 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:

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

## Sources

*This article incorporates material from Safe Prime on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.*