Triangles inside Triangles

This triangle starts with the outside diagonal rows 1, 2, 3, 4, 5, 6, 7, 8,…

The numbers inside the triangle are each the sum of two numbers in the row directly above it: the number diagonally above to the right, and the number diagonally above to the left. For example, 42 = 16 + 26.

Extend the table and determine a relationship between the numbers in the triangle which are exactly divisible by some specific prime greater than 5 . How do the results change if you try another prime greater than 5?