# Chen's Theorem with Small Primes

ORIGINAL ARTICLES

Received:

Accepted:

- 126 Downloads
- 1 Citations

## Abstract

Let is solvable, where

*N*be a sufficiently large even integer. In this paper it is proved that the equation$$
\begin{array}{*{20}c}
{{N = p + P_{2} ,}} & {{p \leqslant N^{{0.95}} ,}} \\
\end{array}
$$

*p*denotes a prime and*P*_{2}denotes an almost prime with at most two prime factors.### Keywords

Chen's theorem Sieve Mean value theorem**MR (2000) Subject Classification**

11N36 ## Preview

Unable to display preview. Download preview PDF.

### References

- 1.Chen, J. R.: 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 (1966)Google Scholar - 2.Chen, J. R.: On the representation of a large even integer as the sum of a prime and the product of at most two primes.
*Sci. Sin.*,**16**, 157–176 (1973)MATHGoogle Scholar - 3.Halberstam, H.: A proof of Chen's Theorem.
*Asterisque*,**24–25**, 281–293 (1975)MathSciNetGoogle Scholar - 4.Chen, J. R.: On the representation of a large even integer as the sum of a prime and the product of at most two primes.
*Sci. Sin.*,**21**, 421–430 (1978)MATHGoogle Scholar - 5.Chen, J. R.: On the representation of a large even integer as the sum of a prime and the product of at most two primes.
*Sci. Sin.*,**21**, 477–494 (1978) (in Chinese)Google Scholar - 6.Lu, M. G., Cai, Y. C.: On Chen's Theorem, to appearGoogle Scholar
- 7.Iwaniec, H.: Rosser's sieve, Recent Progress in Analytic Number Theory II, London: Academic Press, 203–230 (1981)Google Scholar
- 8.Pan, C. D., Pan, C. B.: Goldbach Conjecture, Beijing: Science Press, 175–176 (1992)Google Scholar
- 9.Wu, J.: Theoremes generalises de Bombieri-Vinogradov dans les petits applications, intervalles.
*Quart. J. Math.*, (Oxford),**44**, 109–128 (1993)MATHCrossRefGoogle Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 2002