Chen 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.
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Contents
Definition
A Chen prime is a prime number 
such that 
is either a prime number or is a semiprime, i.e., a product of two primes.
The smaller member of any pair of twin primes is a Chen prime.
Occurrence
Initial values
The ID of the sequence in the Online Encyclopedia of Integer Sequences is A109611
The first few Chen primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409.
The smallest primes that are not Chen primes are: 43, 61, 73, 79, 97.
Proportion of primes
 |
Number of primes  |
Number of Chen primes |
Proportion of primes that are Chen primes |
|---|---|---|---|
| 10 | 4 | 4 | 1 |
| 100 | 25 | 20 | 
|
| 1000 | 168 | ? | ? |
Relation with other properties
Properties for pairs
| Property | Meaning | Comment |
|---|---|---|
| twin primes | primes and |
the lower member of a pair of twin primes is always a Chen prime. The converse doesn't hold, with the smallest counterexample being  .
|
