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 (p ≤ N 0.945) is solvable.
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Cai, Y. C., Chen’s theorem with small primes, Acta Math. Sin. (English Series), 18(3), 2002, 597–604.
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.
Cai, Y. C., On Chen’s theorem (II), J. Number Theory, 128(5), 2008, 1336–1357.
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.
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.
Chen, J. R., On the Goldback’s problem and the sieve methods, Sci. Sin., 21, 1978, 701–739.
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.
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.
Halberstam, H. and Richert, H. E., Sieve Methods, Academic Press, London, 1974.
Iwaniec, H., Rosser’s Sieve, Recent Progress in Analytic Number Theory II, Academic Press, London, 1981, 203–230.
Pan, C. D. and Pan, C. B., Goldbach Conjecture, Science Press, Beijing, 1992, 175–176.
Pan, C. D. and Pan, C. B., Goldbach Conjecture (in Chinese), Science Press, Beijing, 1981, 239–251.
Wu, J., Theoremes generalises de Bombieri-Vinogradov dans les petits applications, intervalles, Quart. J. Math. (Oxford), 44, 1993, 109–128.
Wu, J., Chen’s double sieve, Goldbach’s conjecture and the twin prime problem, Acta Arith., 114, 2004, 215–273.
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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.
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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
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DOI: https://doi.org/10.1007/s11401-011-0645-4