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

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 .