Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Maximal Prime Gaps Supremum and the Firoozbakht's Hypothesis No 30

Version 1 : Received: 29 June 2020 / Approved: 30 June 2020 / Online: 30 June 2020 (10:32:40 CEST)

How to cite: Feliksiak, J. The Maximal Prime Gaps Supremum and the Firoozbakht's Hypothesis No 30. Preprints 2020, 2020060366 (doi: 10.20944/preprints202006.0366.v1). Feliksiak, J. The Maximal Prime Gaps Supremum and the Firoozbakht's Hypothesis No 30. Preprints 2020, 2020060366 (doi: 10.20944/preprints202006.0366.v1).

Abstract

The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers. This paper presents theoretical results which originated with a researchin the subject of the maximal prime gaps. the document presents the sharpest upper bound for the maximal prime gaps ever developed. The result becomes the Supremum bound on the maximal prime gaps and subsequently culminates with the conclusive proof of the Firoozbakht's Hypothesis No 30. Firoozbakht's Hypothesis implies quite a bold conjecture concerning the maximal prime gaps. In fact it imposes one of the strongest maximal prime gaps bounds ever conjectured. Its truth implies the truth of a greater number of known prime gaps conjectures, simultaneously, the Firoozbakht's Hypothesis disproves a known heuristic argument of Granville and Maier. This paper is dedicated to a fellow mathematician, the late Farideh Firoozbakht.

Subject Areas

Cramer's conjecture; elementary proof; Firoozbakht's conjecture; Farideh Firoozbakht; Legendre conjecture; maximal prime gaps Supremum; prime gaps

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