The “N” was used during the period of the 3rd Reich on the headstamps of some 7.9 x 57 and 9 x 19 Patr. 08 rounds, scarcer on the latter than on the former, although not common on either. It probably stands for Nürnberg, as it is always seen in conjunction with RWS ammunition, it seems, and the had a factory at Nürnberg.
The question of “why” remains, for me, unanswered, since Rheinisch Westfälische Sprengstoff used the initials R.W.S. or RWS, on commercial headstamps, and from box labels, we know also on contract ammunition for the German Services. It has usually been thought that it was for the police. Since after a deal with Göring, the Reichsführer-SS was in command of all police as well as the Schutzstaffel, a “police contract” could have been for the SS, although not necessarily so. It could also have been for the Ordnung Politzei, Gestopo (I suppose that would actually be redundant to the SS), or any other police activity of the Reich. Because of the use of RWS, as well as P151 and dnf on military rounds, and because I believe that the “N” was used as a headstamp on the two aforementioned calibers only for one, or a very few production lots, it is interesting and a puzzle to me why it was used so much for components on box labels.
Regarding the “N.S.” for the primer, even though all are NOT marked with the impressed “O” on the cup, it is possible it stands for “Nürnberg” indicating RWS manufacture, with the “S” indicating a Sinoxid primer (non-corrosive). That is simply conjecture on my part. I have no documentation for that opinion.
In short, despite Lew’s confidence in me, I really didn’t answer the question at hand. Simply said the obvious, which wasn’t really stated in any of the other segments of this thread.