The serial number is on old S&W's in FIVE locations- Butt, barrel flat, back of cyl, back of extractor(the side facing the cyl), and back edge of the yoke(you can see it THROUGH one of the chambers if you
wipe the crud off, otherwise take the cyl out of the gun).
The one on the back of the yoke is the one most likely to still be there.
It is a rebuilt or parts gun if the barrel and cyl are not numbered.
The barrel looks like a WW II Victory barrel to me.
The serial number on the butt is NOT factory. It was applied by someone after removing the real number.
Sorry, but it is what it is. If it has sentimental value to you, that will far exceed the market value.