Checking the odd Goldbach conjecture up to
Author:
Yannick Saouter
Journal:
Math. Comp. 67 (1998), 863866
MSC (1991):
Primary 11P32
MathSciNet review:
1451327
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Abstract: Vinogradov's theorem states that any sufficiently large odd integer is the sum of three prime numbers. This theorem allows us to suppose the conjecture that this is true for all odd integers. In this paper, we describe the implementation of an algorithm which allowed us to check this conjecture up to .
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 A.O.L. Atkin and F. Morain, Elliptic curves and primality proving, Math. Comp. 61 (1993), no. 203, 2968. MR 93m:11136
 2.
 J. Brillhart, D.H. Lehmer, and J.L. Selfridge, New primality criteria and factorizations of , Math. Comp. 29 (1975), no. 130, 620647. MR 52:5546
 3.
 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, Kexue Tongbao (1966), no. 17, 385386.
 4.
 J.M. Deshouillers, G.Effinger, H. te Riele, and D.Zinoviev, A complete Vinogradov primes theorem under the Riemann Hypothesis, Preprint, 1997.
 5.
 T. Grandlung, The GNU multiple precision arithmetic library, Technical documentation, 1993.
 6.
 L. Schnirelmann, Über additive Eigenschaften von Zahlen, Math. Ann. (1933), no. 107, 649660.
 7.
 M.K. Sinisalo, Checking the Goldbach conjecture up to , Math. Comp. 61 (1993), no. 204, 931934. MR 94a:11157
 8.
 I.M. Vinogradov, Representation of an odd number as the sum of three primes, Dokl. Akad. Nauk SSSR (1937), no. 15, 169172.
 9.
 T.Z. Wang and J.R. Chen, On odd Goldbach problem under general Riemann hypothesis, Sci. China Ser. A 36 (1993), no. 6, 682691. MR 95a:11090
 10.
 D.Zinoviev, On Vinogradov's constant in Goldbach's ternary problem, J. Number Theory 65 (1997), 334358. CMP 97:16
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Additional Information
Yannick Saouter
Affiliation:
IRISA, Campus de Beaulieu, F35042 Rennes Cédex, France
Email:
Yannick.Saouter@irit.fr
DOI:
http://dx.doi.org/10.1090/S0025571898009284
PII:
S 00255718(98)009284
Keywords:
Odd Goldbach conjecture,
primality tests
Received by editor(s):
March 19, 1996
Received by editor(s) in revised form:
October 16, 1996
Article copyright:
© Copyright 1998
American Mathematical Society
