Help with a puzzle that is a bit too complex

[TheGreatGoatsbie]

I think it's not necessary a problem if two or more pcn overlap. I don't believe you could avoid it. But just one of them may count for fulfilling the rule.

I think pcn/npcn are the right categories for the non-touching rule, but for the placement rule I suggest something else.

Maybe
"Mark 16 diagonally connected pairs of squares (plus 4 single squares?) that do not overlap. Then solve the Sudoku so that the marked pairs (plus ...?) contain each 2-digit (less than 100?) prime number."

Of course just if this is what you mean.

And another thought: If the rules are not ambiguous, it doesn't suit to the fun fact you want to describe. But the Sudoku rules (plus maybe some givens) will solve this problem.

Hmm, I like that way of approaching it, but the marking of the npcn's should also be included. So then it would be:
"Mark 21 pairs of diagonally connected squares and four single square that do not overlap. All primes under hundred have to appear once in these squares. Pairs of squares are read left to right as a two digit prime" 

I don't really follow the last thought, what do you mean exactly?

Thanks for thinking along!