I enjoyed looking at this one too - playing around for a minute on paper with it was fun.

The numbers in each row (when cols is set to 6) are of the form:

6n+1, 6n+2, 6n+3, 6n+4, 6n+5, and 6n+6

Only 6n+1 and 6n+5 can't be trivially factored:

6n+1, 2(3n+1), 3(2n+1), 2(3n+2), 6n+5, 6(n+1)

So it follows that for any n >= 1, numbers in columns 2, 3, 4, and 6 can never be prime. Fun!