Working Paper Article Version 2 This version is not peer-reviewed

Gilbreath Sequences and Proof of Conditions for Gilbreath Conjecture

Version 1 : Received: 6 March 2020 / Approved: 8 March 2020 / Online: 8 March 2020 (17:19:33 CET)
Version 2 : Received: 10 April 2020 / Approved: 12 April 2020 / Online: 12 April 2020 (14:53:47 CEST)

How to cite: Gatti, R. Gilbreath Sequences and Proof of Conditions for Gilbreath Conjecture. Preprints 2020, 2020030145 Gatti, R. Gilbreath Sequences and Proof of Conditions for Gilbreath Conjecture. Preprints 2020, 2020030145

Abstract

The conjecture attributed to Norman L. Gilbreath, but formulated by Francois Proth in the second half of the 1800s, concerns an interesting property of the ordered sequence of prime numbers $P$. Gilbreath conjecture stated that, if we compute the absolute values of differences of consecutive primes on ordered sequence of prime numbers, and if this calculation is repeated for the terms in the new sequence and so on, every sequence will start with 1. In this paper is defined the concept of Gilbreath sequence, Gilbreath triangle and Gilbreath equation. On the basis of the results obtained from the proof of properties, an inductive proof is produced thanks to which it is possible to establish the necessary condition to state that Gilbreath conjecture is true.

Subject Areas

Gilbreath's conjecture; Gilbreth's sequence; sequence; prime numbers; number theory

Comments (1)

Comment 1
Received: 12 April 2020
Commenter: Riccardo Gatti
Commenter's Conflict of Interests: Author
Comment: Improvement of demonstration and clarification of definitions and lemmas
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