Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
Full-text PDF

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 $ [n/2,n - 2]$. We show that 210 is the largest value of n for which this upper bound is attained.


References [Enhancements On Off] (What's this?)

  • [1] J. R. Chen, On the representation of a large even integer as the sum of a prime and the product of at most two primes, Acta Math. Sci. Sinica, I, 16 (1973), 157-176; II, 21 (1978), 421-430. MR 0434997 (55:7959)
  • [2] J. R. Chen and T. Wang, On the odd Goldbach problem, Acta Math. Sci. Sinica 32 (1989), 702-718. MR 1046491 (91e:11108)
  • [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 (R. A. Mollin, ed.), Kluwer Acad., 1989, pp. 423-433. MR 1123087 (93c:11085)
  • [4] H. L. Montgomery and R. C. Vaughan, The exceptional set in Goldbach 's problem, Acta Arith. 27 (1975), 353-370. MR 0374063 (51:10263)
  • [5] O. Ramaré, On Šnirel'man's constant, preprint.
  • [6] H. Riesel and R. C. Vaughan, On sums of primes, Ark. Mat. 21 (1983), 45-74. MR 706639 (84m:10042)
  • [7] J. B. Rosser and L. Schoenfeld, Approximate formulae for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. MR 0137689 (25:1139)
  • [8] L. Šnirel'man, Über additive Eigenschaften von Zahlen, Ann. Inst. Polytechn. Novocerkask 14 (1930), 3-28; and Math. Ann. 107 (1933), 649-690. MR 1512821
  • [9] I. M. Vinogradov, Representation of an odd number as a sum of three primes, C.R. Acad. Sci. URSS 15 (1937), 6-7.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11P32, 11Y11

Retrieve articles in all journals with MSC: 11P32, 11Y11


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1202609-9
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society