Definition:Chen Prime

Definition

A Chen Prime is a prime number $p$ such that $p + 2$ is either a prime number or a semiprime.

The even integer $2 p + 2$ then satisfies Chen's Theorem.

The first few Chen primes are

$2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, \ldots$

This sequence is A109611 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

The first few non-Chen primes are

$43, 61, 73, 79, 97, 103, 151, 163, 173, 193, 223, 229, 241, \ldots$

This sequence is A102540 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

• Infinite Number of Chen Primes

Source of Name

This entry was named for Chen Jingrun.

Sources

• Andersen, Jens Kruse. "Chen Prime." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ChenPrime.html