|Named after||Chen Jingrun|
|Author of publication||Chen, J. R.|
|First terms||2, 3, 5, 7, 11, 13|
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 A109611 in the OEIS).
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.
2996863034895 × 21290000 − 1, with 388342 decimal digits, is the largest known Chen prime as of March 2018[update].
The sum of the reciprocals of Chen primes converges.
Green and Tao showed that the Chen primes contain infinitely many arithmetic progressions of length 3. Binbin Zhou generalised this result by showing that the Chen primes contain arbitrarily long arithmetic progressions.
- 1.^ Chen primes were first described by Yuan, W. On the Representation of Large Even Integers as a Sum of a Product of at Most 3 Primes and a Product of at Most 4 Primes[permanent dead link], Scienca Sinica 16, 157-176, 1973.
- Chen, J. R. (1966). "On the representation of a large even integer as the sum of a prime and the product of at most two primes". Kexue Tongbao. 17: 385–386.
- Prime Curios! page on 59
- Ben Green and Terrence Tao, Restriction theory of the Selberg sieve, with applications, Journal de Théorie des Nombres de Bordeaux 18 (2006), pp. 147–182.
- Binbin Zhou, The Chen primes contain arbitrarily long arithmetic progressions, Acta Arithmetica 138:4 (2009), pp. 301–315.
- The Prime Pages
- Green, Ben; Tao, Terence (2006). "Restriction theory of the Selberg sieve, with applications". Journal de théorie des nombres de Bordeaux. 18 (1): 147–182. arXiv:math.NT/0405581. doi:10.5802/jtnb.538.
- Weisstein, Eric W. "Chen Prime". MathWorld.
- Zhou, Binbin (2009). "The Chen primes contain arbitrarily long arithmetic progressions". Acta Arith. 138 (4): 301–315. Bibcode:2009AcAri.138..301Z. doi:10.4064/aa138-4-1.