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 as the lower member of a pair of twin primes is by definition a Chen prime. 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, … (sequence in the OEIS). The first few Chen primes that are not the lower member of a pair of twin primes are 2, 7, 13, 19, 23, 31, 37, 47, 53, 67, 83, 89, 109, 113, 127, ... (sequence in the OEIS). The first few non-Chen primes are 43, 61, 73, 79, 97, 103, 151, 163, 173, 193, 223, 229, 241, … (sequence in the OEIS). All of the supersingular primes are Chen primes. discovered the following 3 × 3 magic square of nine Chen primes: As of March 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges. (Wikipedia).
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