How about a bit more info? Like which type of Luger and the date of manufacture. That would reduce the guesswork!
At the moment (guessing):
S. probably stands for "Schutzpolizei", i.e. it is a police pistol.
Hn. could be Hanau (which is in Hessen)
I. is "Schutzbereich 1" i.e. first police division/area.
4. is "Hundertschaft" number 4. A "Hundertschaft" is roughly equivalent to a company.
112. is weapon number 112.