References
van der Corput, J. G.: On de Polignac's conjecture. Simon Stevin27, 99–105 (1950)
Davenport, H.: Multiplicative number theory. Chicago: Markham 1967
Erdös, P.: On integres of the form 2k+p and some related problems. Summa Brasil. Math.2, 113–123 (1950)
Gallagher, P. X.: A large sieve density estimate near σ=1. Inventiones math.11, 329–339 (1970)
Hardy, G. H., Wright, E. M.: An introduction to the theory of numbers. 4th ed. Oxford: Clarendon Press 1965
Lavrik, A. F.: On a theorem in the additive theory of numbers. Uspehi Mat. Nauk14, 197–198 (1951)
Linnik, Ju. V: Prime numbers and powers of two. Trudy Mat. Inst. Steklov38, 151–169 (1951)
Linnik, Ju. V.: Addition of prime numbers and powers of one and the same number. Mat. Sbornik (N. S.)32, 3–60 (1953)
Montgomery, H. L.: Topics in multiplicative number theory. Lecture Notes in Mathematics227. Berlin-Heidelberg-New York: Springer 1971
Montgomery, H. L., Vaughan, R. C.: On the exceptional set in Goldbach's problem. Acta Arith.27, 353–370 (1975)
Page, A.: On the number of primes in an arithmetic progression. Proc. London Math. Soc.39, 116–141 (1935)
de Polignac, A.: Six propositions arithmologiques déduites du crible d'Ératosthène. Nouv. Ann. Math.8, 423–429 (1849)
Postnikov, A. G.: Ergodic problems in the theory of congruences and of diophantine approximations. Proc. Steklov Inst. Math.82 (1966)
Prachar, K.: Primzahlverteilung. Berlin-Göttingen-Heidelberg: Springer 1957
Romonoff, N. P.: Über einige sätze der additiven Zahlentheorie. Math. Ann.57, 668–678 (1934)
Suetuna, Z.: Bemerkung über das Product vonL-Functionen. Tohoku Math. J.27, 248–257 (1926)
Vaughan, R. C.: On Goldbach's problem. Acta Arith.22, 21–48 (1972)
Vinogradov, A. I.: On an “almost binary” problem. Izv. Akad. Nauk SSSR, Ser. Mat.20, 713–750 (1956)
Vinogradov, I. M.: The method of trigonometric sums in the theory of numbers, revised and annotated by K. F. Roth and Anne Davenport. New York: Interscience 1954
Crocker, R.: On the sum of a prime and of two powers of two. Pacific J. Math.36, 103–107 (1971)
de Polignac, A.: Recherches nouvelles sur les nombres primiers. C. R. Acad. Sci. Paris29, 397–401, 738–739 (1849)
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Gallagher, P.X. Primes and powers of 2. Invent Math 29, 125–142 (1975). https://doi.org/10.1007/BF01390190
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DOI: https://doi.org/10.1007/BF01390190