Parikh Prime Words and GO-like Territories

An n-dimensional vector of natural numbers is said to be prime if the greatest common divisor of its components is one. A word is said to be Parikh prime if its Parikh vector is prime. The languages of Parikh prime and of Parikh non-prime words are investigated (they are neither semilinear nor slender, hence are not context-free or DOL languages; both of them can be generated by matrix grammars with appearance checking).