Safe prime

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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


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.


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 OEIS

The 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

Related properties of longer chains of primes