Abstract
It is proved that every sufficiently large even integer can be represented as a sum of two primes and at most 2250 powers of 2.
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Linnik, Y. V., Prime numbers and powers of two,Trudy Mat. Isnt. Steklov, 1951, 38: 151.
Linnik, Y. V., Addition of prime numbers and powers of one and the same number,Mat. Sb. (N. S.), 1953, 32: 3.
Liu, J. Y., Liu, M. C., Wang, T. Z., On the number of powers of 2 in a representation of large even integers (II),Sci. in China, 1998, 41(4): 802.
Liu, J. Y., Liu, M. C., Wang, T. Z., On the number of powers of 2 in a representation of large even integers (I),Sci. in China, 1998, 41(4): 386.
Gallagher, P. X., Primes and powers of 2,Invent. Math., 1975, 29: 125.
Heath-Brown, D. R., Zero free regions for DirichletL-functions, and the least prime in an arithmetic progression,Proc. London Math. Soc., 1992, 64: 265.
Liu, M. C., Tsang, K. M., Small prime solutions of linear equations, Théorie des Nombres (eds. De Koninck, J. M., Levesque, C.), Berlin: de Gruyter, 1989, 595–624.
Hasse, H., Vorlesungen über Zahlentheorie,Grundlehren Math. Wiss. Band 59, Berlin and New York: Springer-Verlag, 1964.
Pan, C. D., Pan, C. B.,Goldbach Conjecture, Beijing: Science Press, 1992.
Jutila, M., On Linnik’s constant,Math. Scand., 1977, 41: 45.
Chen, J. R., The exceptional set of Goldbach numbers,Scientia Sinica (Sci. in China), 1983, 26(7): 714.
Gallagher, P. X., A large sieve estimate nearσ = 1,Invent. Math., 1970, 11: 329.
Halberstam, H., Richert, H. E.,Sieve Methods, London: Academic Press, 1974.
Davenport, H.,Multiplicative Number Theory, 2nd ed., New York: Springer-Verlag, 1980.
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Project supported partially by the National Natural Science Foundation of China (Grant No. 19771029).
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Wang, T. On Linnik’s almost Goldbach theorem. Sci. China Ser. A-Math. 42, 1155–1172 (1999). https://doi.org/10.1007/BF02875983
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DOI: https://doi.org/10.1007/BF02875983