Good question ken! So far as I can tell, a Sierpinski triangle can be created by blacking out all of the even numbers in Pascal's triangle.

Ton's of patterns can be found in Pascal's triangle, not only primes, but Fibonacci numbers, square numbers and more. For example, look at all of the rows that have a prime number as their 2nd element. All of the other numbers in that row are divisible by that prime!
There's a lot of interconnectedness in mathematics, and all things.