CONFIRMATION OF THE FIROOZBAKHT CONJECTURE AND DEDUCTION OF THE ANDRICA, CRAMER AND SINHA CONJECTURES WITH SOME OTHER IMPORTANT CONSQUENCES

I confirm, in the present short paper, the Firoozbakht conjecture, remained open since 1982. Recall that this conjecture is one of the Neil Sloane unsolved prime conjectures list. My Proof of the Firoozbakht conjecture is very simple and uses elementary tools of mathematics. Some important consequences, such as the Andrica (remained open since 1986), Cramér (remained open since 1936) and Sinha (remained open since 2018) conjectures are deduced from the Firoozbakht conjecture. The Deduction is based on the Taylor formula, the intermediate value theorem, the L’Hôpital rule, the Dursat theorem and the growth properties of some elementary functions.

Keywords

Firoozbakht conjecture-Prime Number theorem-The intermediate value theorem-A decreasing function-An increasing function-Dusart theorem-Euclid Theorem-equivalent sequences-Andrica conjecture-Cramer conjecture-Sinha conjecture-Taylor formula with Lagrange rest 2010 Mathematics Subject Classification: 11 A xx (Elementary Number Theory).

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