An upper bound in Goldbach's problem

Authors:
Jean-Marc Deshouillers, Andrew Granville, Władysław Narkiewicz and Carl Pomerance

Journal:
Math. Comp. **61** (1993), 209-213

MSC:
Primary 11P32; Secondary 11Y11

DOI:
https://doi.org/10.1090/S0025-5718-1993-1202609-9

MathSciNet review:
1202609

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Abstract | References | Similar Articles | Additional Information

Abstract: It is clear that the number of distinct representations of a number *n* as the sum of two primes is at most the number of primes in the interval . We show that 210 is the largest value of *n* for which this upper bound is attained.

**[1]**Jing Run Chen,*On the representation of a larger even integer as the sum of a prime and the product of at most two primes*, Sci. Sinica**16**(1973), 157–176. MR**0434997****[2]**Jing Run Chen and Tian Ze Wang,*On the Goldbach problem*, Acta Math. Sinica**32**(1989), no. 5, 702–718 (Chinese). MR**1046491****[3]**A. Granville, J. van de Lune, and H. J. J. te Riele,*Checking the Goldbach conjecture on a vector computer*, Number theory and applications (Banff, AB, 1988) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 265, Kluwer Acad. Publ., Dordrecht, 1989, pp. 423–433. MR**1123087****[4]**H. L. Montgomery and R. C. Vaughan,*The exceptional set in Goldbach’s problem*, Acta Arith.**27**(1975), 353–370. Collection of articles in memory of Juriĭ Vladimirovič Linnik. MR**0374063**, https://doi.org/10.4064/aa-27-1-353-370**[5]**O. Ramaré,*On Šnirel'man's constant*, preprint.**[6]**H. Riesel and R. C. Vaughan,*On sums of primes*, Ark. Mat.**21**(1983), no. 1, 46–74. MR**706639**, https://doi.org/10.1007/BF02384300**[7]**J. Barkley Rosser and Lowell Schoenfeld,*Approximate formulas for some functions of prime numbers*, Illinois J. Math.**6**(1962), 64–94. MR**0137689****[8]**L. Schnirelmann,*Über additive Eigenschaften von Zahlen*, Math. Ann.**107**(1933), no. 1, 649–690 (German). MR**1512821**, https://doi.org/10.1007/BF01448914**[9]**I. M. Vinogradov,*Representation of an odd number as a sum of three primes*, C.R. Acad. Sci. URSS**15**(1937), 6-7.

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1202609-9

Article copyright:
© Copyright 1993
American Mathematical Society