Rudolf Ondrejka discovered the following 3 × 3 magic square of nine Chen primes:[2] As of March 2018[update], the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits.
The sum of the reciprocals of Chen primes converges.
[citation needed] Chen also proved the following generalization: For any even integer h, there exist infinitely many primes p such that p + h is either a prime or a semiprime.
Ben Green and Terence Tao showed that the Chen primes contain infinitely many arithmetic progressions of length 3.
[3] Binbin Zhou generalized this result by showing that the Chen primes contain arbitrarily long arithmetic progressions.