For 3 tuples and 4 tuples we only need to consider divisibility by 2 and 3. We do not need to bother with divisibility by 5. So 3 tuples and 4 tuples can be all prime numbers if all the numbers are congruent to 1 or 5 modulo 6.
We say that x is relatively prime to 6 if and only if x is congruent to 1 or 5 mod 6.
Regards
Matt
