The theorem of the primal radius

Jamel Ghannouchi (1)

1 ESSTT - Ecole Supérieure des Sciences et Techniques [Tunis]

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 $2x'=(x'+r')-(r'-x')$.

Mots clés: Primal radius; Goldbach; de Polignac

Domaines: Mathématiques générales [math.GM]

Jamel Ghannouchi. The theorem of the primal radius. 2011. ⟨hal-00677734⟩