Checking the odd Goldbach conjecture up to

Author:
Yannick Saouter

Journal:
Math. Comp. **67** (1998), 863-866

MSC (1991):
Primary 11P32

MathSciNet review:
1451327

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Abstract | References | Similar Articles | Additional Information

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 .

**1.**A. O. L. Atkin and F. Morain,*Elliptic curves and primality proving*, Math. Comp.**61**(1993), no. 203, 29–68. MR**1199989**, 10.1090/S0025-5718-1993-1199989-X**2.**John Brillhart, D. H. Lehmer, and J. L. Selfridge,*New primality criteria and factorizations of 2^{𝑚}±1*, Math. Comp.**29**(1975), 620–647. MR**0384673**, 10.1090/S0025-5718-1975-0384673-1**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, 385-386.**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, 649-660.**7.**Matti K. Sinisalo,*Checking the Goldbach conjecture up to 4⋅10¹¹*, Math. Comp.**61**(1993), no. 204, 931–934. MR**1185250**, 10.1090/S0025-5718-1993-1185250-6**8.**I.M. Vinogradov,*Representation of an odd number as the sum of three primes*, Dokl. Akad. Nauk SSSR (1937), no. 15, 169-172.**9.**Tian Ze Wang and Jing Run Chen,*On odd Goldbach problem under general Riemann hypothesis*, Sci. China Ser. A**36**(1993), no. 6, 682–691. MR**1246313****10.**D.Zinoviev,*On Vinogradov's constant in Goldbach's ternary problem*, J. Number Theory**65**(1997), 334-358. CMP**97:16**

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Additional Information

**Yannick Saouter**

Affiliation:
IRISA, Campus de Beaulieu, F-35042 Rennes Cédex, France

Email:
Yannick.Saouter@irit.fr

DOI:
http://dx.doi.org/10.1090/S0025-5718-98-00928-4

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