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 . We show that 210 is the largest value of *n* for which this upper bound is attained.

**[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.

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