You may also find the correct SN stamped on a flat on the bottom of the barrel and on the rear face of the cylinder. Could also be stamped or penciled on the inside surface of the right grip panel. All should match.
The P may be added for some reason. Does it look different from the D? In the 1970s Model 10s did use a D prefix number. Open the cylinder for the model number like MOD 10-7 or similar. May also find the correct serial there.