Schnirelmann Constant

The constant s_0 in Schnirelmann's theorem such that every integer >1 is a sum of at most s_0 primes. Of course, by Vinogradov's theorem, it is known that 4 primes suffice for all sufficiently large numbers, but this constant gives a sufficient number for all numbers. The best current estimate is s_0=7 (Ramaré 1995), and a summary of progress on upper bounds for s_0 is summarized in the following table.

7Ramaré (1995)
19Riesel and Vaughan (1983)
26Deshouillers (1977)
27Vaughan (1977)
55Klimov (1975)
115Klimov et al. (1972)
159Deshouillers (1973)

See also

Schnirelmann's Theorem, Waring's Problem

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Deshouillers, J.-M. No. 17 in "Amélioration de la constante de Šnirelman dans le probléme de Goldbach." Séminaire Delange-Pisot-Poitou (14e année: 1972/73). Théorie des nombres: Fascicule 2: Exposés 17 à 26, et Groupe d'étude. Paris: Secrétariat Mathématique, pp. 1-4, 1973.Deshouillers, J.-M. "Sur la constante de Šnirel'man." No. G16 in Séminaire Delange-Pisot-Poitou, 17e année (1975/76). Théorie des nombres: Fascicule 2: Exposés 23 à 31 et Groupe d'étude. Paris: Secrétariat Math., pp. 1-6, 1977.Klimov, K. I. Naucn. Trudy Kuibysev Gos. Ped. Inst. 158, 14-30, 1975.Klimov, N. I.; Pil'tjaĭ, G. Z.; and Šeptickaja, T. A. "An Estimate of the Absolute Constant in the Goldbach-Šnirel'man Problem." In Issledovaniya po teorii chisel, Vyp. 4. [Studies in number theory, No. 4] (Ed. N. Lenskoĭ). Saratov: Izdat. Saratov. Univ., pp. 35-51, 1972.Ramaré, O. "On Šnirel'man's Constant." Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22, 645-706, 1995.Riesel, H. and Vaughan, R. C. "On Sums of Primes." Ark. Mat. 21, 46-74, 1983.Vaughan, R. C. "On the Estimation of Schnirelman's Constant." J. reine angew. Math. 290, 93-108, 1977.

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Schnirelmann Constant

Cite this as:

Weisstein, Eric W. "Schnirelmann Constant." From MathWorld--A Wolfram Web Resource.

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