Chen prime

A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2p + 2 therefore satisfies Chen's theorem.

The Chen primes are named after Chen Jingrun, who proved in 1966 that there are infinitely many such primes. This result would also follow from the truth of the twin prime conjecture.

The first few Chen primes are

The first few Chen primes that are not the lower member of a pair of twin primes are

The first few non-Chen primes are

All of the supersingular primes are Chen primes.

Rudolf Ondrejka discovered the following 3x3 magic square of nine Chen primes:

The lower member of a pair of twin primes is by definition a Chen prime. Thus, 3756801695685*2⁶⁶⁶⁶⁶⁹ - 1 (having 200700 decimal digits), found by Primegrid, represents the largest known Chen prime as of December 25, 2011.

The largest known Chen prime at that time which is not a twin prime was (1284991359*2⁹⁸³⁰⁵+1)*(96060285*2¹³⁵¹⁷⁰+1)-2 (having 70301 decimal digits).