HAL : hal-00677734, version 1
 The theorem of the primal radius
 (2011)
 The present algebraic development begins simply by an exposition of the data of the problem. Our calculus is supported by a reasoning which must conduct to an impossibility. We define the primal radius : For all \$x\$ an integer greater or equal to \$3\$, we define a primal number \$r\$ for which \$x-r\$ and \$x+r\$ are prime numbers. We see then that Goldbach conjecture would be verified because \$2x=(x+r)+(x-r)\$. We prove the existence of \$r\$ for all \$x\geq{3}\$. We prove also the existence, for all \$x'\$ an integer, of a primal radius \$r'\$ for which \$x'+r'\$ and \$r'-x'\$ are prime numbers strictly greater than \$2\$. De Polignac conjecture would be quickly verified because \$2x'=(x'+r')-(r'-x')\$.
 1 : Ecole Supérieure de Science et Technique de Tunis (ESSTT) Ministère de l'Enseignement Supérieur et de la Recherche Scientifique
 Domaine : Mathématiques/Mathématiques générales
 Mots Clés : Primal radius – Goldbach – de Polignac
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 hal-00677734, version 1 http://hal.archives-ouvertes.fr/hal-00677734 oai:hal.archives-ouvertes.fr:hal-00677734 Contributeur : Jamel Ghannouchi <> Soumis le : Vendredi 9 Mars 2012, 14:01:49 Dernière modification le : Vendredi 9 Mars 2012, 14:03:49