# FINDING AND CREATING COMPLEX PATTERNS IN GILBREATH'S CONJECTURE

## Description

We know that there is a variety of patterns in triangles in number theory. The Gilbreath's triangle is shaped by subtracting two numbers from the starting row above. The first row is made out of consecutive prime numbers. There are a lot of similarities to Pascal's and Sierpinski's triangle, but we are not able to work with their data. The conjecture is that through the making of the lower rows we can only see one pattern, a series of 1s on the left side of the triangle. We proved that by adding more characters in the first row, but with same nature as the initial ones, some numerical patterns appear.We found that there are actually a lot of different patterns in Gilbreath's triangle. We showed the full formation of the triangle algebraically and geometrically , in order that the reader understands the conjecture. This conjecture remains unsolved since 1958 till now. But this paper has significant contribution to the possible future solution-disproof and further analysis of Gilbreath's conjecture.