Chen's theorem

From Wikipedia, the free encyclopedia

Chen's theorem was first stated by Chinese mathematician Chen Jing Run in 1966^[1], with further details of the proof in 1973^[2]. His original proof was much simplified by P. M. Ross^[3]. The theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes). Chen's theorem is a giant step towards the Goldbach conjecture, and a remarkable result of the sieve methods.

[edit] External links

• Almost twin primes and Chen's theorem
• Chen's Theorem -- from MathWorld

[edit] References

1. ^ J. R. Chen, 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 (1966), 385-386.
2. ^ J. R. Chen, On the representation of a larger even integer as the sum of a prime and the product of at most two primes, Sci. Sinica 16 (1973), 157-176.
3. ^ P. M. Ross, On Chen's theorem that each large even number has the form (p₁+p₂) or (p₁+p₂p₃), J. London Math. Soc. (2) 10 (1975), no. 4, 500--506.