An Elementary Proof of Gilbreaths Conjecture

Abstract

Given the fact that the Gilbreath's Conjecture has been a major topic of research in Aritmatic progression for well over a Century,and as bellow:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2
1 0 2 2 2 2 2 2 4 4 2 2 2 2 0 4
1 2 0 0 0 0 0 2 0 2 0 0 0 2 4
1 2 0 0 0 0 2 2 2 2 0 0 2 2
1 2 0 0 0 2 0 0 0 2 0 2 0
1 2 0 0 2 2 0 0 2 2 2 2
1 2 0 2 0 2 0 2 0 0 0
1 2 2 2 2 2 2 2 0 0
1 0 0 0 0 0 0 2 0
1 0 0 0 0 0 2 2
1 0 0 0 0 2 0
1 0 0 0 2 2
1 0 0 2 0
1 0 2 2
1 2 0
1 2
1
The Gilbreath's conjecture in a way as easy and comprehensive as possible.
He proposed that these differences, when calculated repetitively and left as bsolute values, would always result in a row of numbers beginning with 1,In this paper we bring elementary proof for this conjecture.