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2010-05-03T20:31:55Z

Created page with '{{prime number property}} ==Definition== A '''Chen prime''' is a prime number <math>p</math> such that <math>p + 2</math> is either a prime number or is a semiprime, i.…'

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{{prime number property}}

==Definition==

A '''Chen prime''' is a [[prime number]] <math>p</math> such that <math>p + 2</math> 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===

{{oeis|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===

{| class="wikitable" border="1"
! <math>n</math> !! Number of primes <math>\le n</math> !! Number of Chen primes <math>\le n</math> !! Proportion of primes that are Chen primes
|-
| 10 || 4 || 4 || 1
|-
| 100 || 25 || 20 || <math>4/5 = 0.8</math>
|-
| 1000 || 168 || ? || ?
|}

==Relation with other properties==

===Properties for pairs===

{| class="wikitable" border="1"
! Property !! Meaning !! Comment
|-
| [[twin primes]] || primes <math>p</math> and <math>p + 2</math> || the lower member of a pair of twin primes is always a Chen prime. The converse doesn't hold, with the smallest counterexample being <math>(7,9)</math>.
|}

Chen prime - Revision history

Vipul: Created page with '{{prime number property}} ==Definition== A '''Chen prime''' is a prime number p such that p + 2 is either a prime number or is a semiprime, i.…'

Vipul: Created page with '{{prime number property}} ==Definition== A '''Chen prime''' is a prime number $p$ such that $p + 2$ is either a prime number or is a semiprime, i.…'