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

Authors

  • Mohammed Ghanim Author

Keywords:

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

Abstract

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.

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Published

2020-08-10

Issue

Vol. 7 No. 8 (2020)

Section

Articles

How to Cite

CONFIRMATION OF THE FIROOZBAKHT CONJECTURE AND DEDUCTION OF THE ANDRICA, CRAMER AND SINHA CONJECTURES WITH SOME OTHER IMPORTANT CONSQUENCES. (2020). Global Journal of Advanced Engineering Technologies and Sciences, 7(8), 11-24. https://gjaets.com/index.php/gjaets/article/view/26