Gilbreath Sequences and Proof of Conditions for Gilbreath Conjecture

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 the concept of Gilbreath sequence, Gilbreath triangle and Gilbreath equation are defined and on the basis of the results obtained from their properties, an inductive proof is produced, which establishes the necessary condition to state that Gilbreath conjecture is true.