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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.

s_0author
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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References

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. https://mathworld.wolfram.com/SchnirelmannConstant.html

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