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
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.
