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Checking the odd Goldbach conjecture up to 10 20
 Math. Comp
, 1998
"... Abstract. Vinogradovâ€™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 conje ..."
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Abstract. Vinogradovâ€™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 10 20. 1.
Improved Bounds for Goldback Conjecture
"... : Goldach's conjecture states that every even integer greater or equal to 6 is the sum of two prime numbers. This result is still unproved. This conjecture has been numerically checked up to 4:10 11 on an IBM 3083 mainframe. We describe here an implementation on a less powerful machine which raise ..."
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: Goldach's conjecture states that every even integer greater or equal to 6 is the sum of two prime numbers. This result is still unproved. This conjecture has been numerically checked up to 4:10 11 on an IBM 3083 mainframe. We describe here an implementation on a less powerful machine which raises the bound to 10 12 . Keywords: Prime numbers; Goldbach's problem (R'esum'e : tsvp) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universit e de Rennes 1  Insa de Rennes et en Automatique  unit e de recherche de Rennes Am'eliorations de bornes au sujet de la conjecture de Goldbach (premi`ere version) R'esum'e : La conjecture de Goldbach stipule que tout nombre pair sup'erieur ou 'egal `a 6 est somme de deux nombres premiers. Ce r'esultat est `a ce jour non d'emontr'e. Il a 'et'e v'erifi'e num'eriquement jusqu'`a 4:10 11 sur un IBM 3083. Nous d'ecrivons ici une impl'ementation...