calculus and analysis – Finding the row and position number in Pascal’s Triangle

I have the following code:

(Alpha) = 100;
(DoubleStruckCapitalT)(i_, j_) := Binomial(i, j - 1); 
  If(PrimeQ((DoubleStruckCapitalT)(n, k)), {n, 
    k, (DoubleStruckCapitalT)(n, k)}, Nothing), {n, 0, (Alpha)}, {k,
    1, (Alpha)}) //. {} -> Nothing

Now, this code uses the function $T(n,k)$ where $n$ is the number of the row of pascals triangle and $k$ is the position number. Outside of the triangle $T(n,k)$ always gives a $0$. When I want to compute the code of mine for big values of (Alpha) it has to check all the rows for that number of inputs but the 0’th row only have one position that is not equal to $0$ and so on. How can I edit my code such that it only checks the numbers that matter instead of the large amount of zeros?