Ok going back to the mathematica version that does it the slower primality testing per terms in cell way I am seeing the deviations meaning the gcd triangle is not an exact match to what we have here.

Here is the code on GitHub - it renders it correctly and addresses the issues. Https://GitHub.com/shaunxcode/a-pattern-in-the-primes

From OP: > Interestingly, this same pattern holds for more numbers, and for different intervals.

He's not claiming it holds for _all_ n, just for _many_ n.

I think you may misunderstand what terms are in a cell. For instance in your first example what numbers live there? In that observable you can run cellToTerms(row,n,binomialCoEfficient2,col) to get the terms. You can then chain .map(isPrime) (for reasonable sizes it is slurping in data to make testing faster). Those fns are there for interactivity I have not gotten around to adding yet.

Those are some pretty basic checks to miss. Perhaps I've misread OP's claim.