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

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Abstract : 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 .
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Cited literature [5 references]

https://hal.archives-ouvertes.fr/hal-01356061
Contributor : Mohamed Sghiar <>
Submitted on : Thursday, November 3, 2016 - 11:19:20 AM
Last modification on : Monday, April 9, 2018 - 12:20:05 PM
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M 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. ⟨http://www.pspchv.com/content_PJNTA-vol-10-issues-1-2.html⟩. ⟨hal-01356061⟩

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