DES APPLICATIONS GÉNÉRATRICES DES NOMBRES PREMIERS ET CINQ PREUVES DE L’HYPOTHÈSE DE RIEMANN

Mohamed Sghiar (1)

1 Chercheur indépendant

I will prove that there exists one application $\psi(\psi^-,\psi^+)$ on $\mathbb{R}^2$ such that $\mathcal{P} = \{\pm2,\pm3 \} \cup 6\times\mathcal{F^-}+1 \cup6\times\mathcal{F^+}-1$ where : $ \mathcal {P} $ is the set of relatively prime numbers, $\mathcal{F^-} = \mathbb{Z}\cap( \psi^+ ( \mathbb{Z}^*\times \mathbb{Q}\backslash\mathbb{Z})\backslash \psi^+(\mathbb{Z}^*\times \mathbb{Z}^*))$ and $\mathcal{F^+} =\mathbb{Z}\cap( \psi^- ( \mathbb{Z}^*\times \mathbb{Q}\backslash\mathbb{Z})\backslash \psi^-(\mathbb{Z}^*\times \mathbb{Z}^*) )$. And I will give an algorithm that allows both to generate prime numbers and confirm that $ \mathcal {P} $ is indeed determined by the mapping $ \psi (\psi ^ - , \psi ^ +) $ that I will apply in some proofs of the Riemann hypothesis .

Mots clés: Prime number; Riemann hypothesis; l'Hypothèse de Riemann; zeta function; fonction zeta de Riemann

Domaines: Théorie des nombres [math.NT]

Mohamed Sghiar. DES APPLICATIONS GÉNÉRATRICES DES NOMBRES PREMIERS ET CINQ PREUVES DE L’HYPOTHÈSE DE RIEMANN . Pioneer Journal of Algebra Number Theory and its Applications, 2015, 10 (1-2), pp.1-31. ⟨hal-01251577⟩