Skip to main content
Log in

Chen’s theorem with small primes

  • Published:
Chinese Annals of Mathematics, Series B Aims and scope Submit manuscript

Abstract

Let N be a sufficiently large even integer. Let p denote a prime and P 2 denote an almost prime with at most two prime factors. In this paper, it is proved that the equation N = p + P 2 (pN 0.945) is solvable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cai, Y. C., Chen’s theorem with small primes, Acta Math. Sin. (English Series), 18(3), 2002, 597–604.

    Article  MATH  Google Scholar 

  2. Cai, Y. C. and Lu, M. G., On Chen’s Theorem, Analytic Number Theory, Beijing/Kyoto, 1999, 99–119, Dev. Math., Vol. 6, Kluwer Acad. Publ., Dordrecht, 2002.

    MATH  Google Scholar 

  3. Cai, Y. C., On Chen’s theorem (II), J. Number Theory, 128(5), 2008, 1336–1357.

    Article  MathSciNet  Google 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, Kexue Tongbao, 17, 1966, 385–386.

    Google 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., 16, 1973, 157–176.

    MATH  Google Scholar 

  6. Chen, J. R., On the Goldback’s problem and the sieve methods, Sci. Sin., 21, 1978, 701–739.

    MATH  Google Scholar 

  7. 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 (II), Sci. Sin., 21, 1978, 421–430.

    MATH  Google Scholar 

  8. 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 (II) (in Chinese), Sci. Sin., 21, 1978, 477–494.

    Google Scholar 

  9. Halberstam, H. and Richert, H. E., Sieve Methods, Academic Press, London, 1974.

    MATH  Google Scholar 

  10. Iwaniec, H., Rosser’s Sieve, Recent Progress in Analytic Number Theory II, Academic Press, London, 1981, 203–230.

    Google Scholar 

  11. Pan, C. D. and Pan, C. B., Goldbach Conjecture, Science Press, Beijing, 1992, 175–176.

    MATH  Google Scholar 

  12. Pan, C. D. and Pan, C. B., Goldbach Conjecture (in Chinese), Science Press, Beijing, 1981, 239–251.

    Google Scholar 

  13. Wu, J., Theoremes generalises de Bombieri-Vinogradov dans les petits applications, intervalles, Quart. J. Math. (Oxford), 44, 1993, 109–128.

    Article  MATH  Google Scholar 

  14. Wu, J., Chen’s double sieve, Goldbach’s conjecture and the twin prime problem, Acta Arith., 114, 2004, 215–273.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yingchun Cai.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11071186), the Science Foundation for the Excellent Youth Scholars of Shanghai (No. ssc08017) and the Doctoral Research Fund of Shanghai Ocean University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Y., Cai, Y. Chen’s theorem with small primes. Chin. Ann. Math. Ser. B 32, 387–396 (2011). https://doi.org/10.1007/s11401-011-0645-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-011-0645-4

Keywords

2000 MR Subject Classification

Navigation