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 434997
- [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. MR 374063, 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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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1993-1202609-9
Article copyright:
© Copyright 1993
American Mathematical Society