# Safe prime

From Number

This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.

View other properties of prime numbers | View other properties of natural numbers

## Contents

## Definition

A prime number is termed a **safe prime** if is odd and is also a prime number.

The corresponding prime is termed a Sophie Germain prime.

## Occurrence

### Initial values

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A005385

The first few safe primes are:

5, 7, 11, 23, 47, 59, 83, 107, 167, [SHOW MORE]View list on OEISThe first few primes that are *not* safe primes are: 2, 3, 13, 17, 19.

### Density in primes

Cutoff | Number of primes | Number of safe primes | Proportion of primes that are safe primes |
---|---|---|---|

10 | 4 | 2 | |

100 | 25 | 7 | |

1000 | 168 | 24 |

## Relation with other properties

### Related properties of primes or pairs of primes

- Sophie Germain prime is a prime such that is also a prime.
- Twin primes are primes that differ by two.

### Related properties of longer chains of primes

- Cunningham chain of the first kind is a chain of primes such that .
- Bitwin chain is a collection of multiple pairs of twin primes, each pair being double the previous one.