Ithaca M37s are awesome!
As previously stated, the 37s are all Featherlights. They are a very lightweight and svelte, sexy gun. They are very simple, but built out of great steel and just about bombproof.
To the OP, if the barrel fits the gun well, send your barrel to
Guncat to have it cut. Also, your SN looks to be a 1973 vintage number (from Walter Snyder's book 1973 = 371287501 – 371366000). Of note, in 1969 when they got to the millionth SN they added the model number (37) in front of it, hence the 371xxxxxx SNs.
Prior to 1963 Ithaca matched their barrels to the receiver and both were marked with the serial number. Its not the end of the world is the two numbers don't match, there "might" be some "possible" headspace problems; something a good smith can check for. Sometime in 1963 Ithaca changed gears a bit and supposedly the barrels were all interchangeable after that. Not necessarily so, I've come across a bunch built after 1963 that could use some "fitting" ...they still work fine though.
As cool as the 37s are, there just doesn't seem to be a big demand for them; they can still be had off places like gunbroker for a couple hundred bucks (my 1956 vintage 16ga was $111). Just gotta keep your eye out.
They do have a few drawbacks. There is NO port-loading a 37. You can try all you want, but in the end, its always much faster to just put the shell into the magazine and pump the action. Watch all the youtube vids you like and talk to and watch all the know-it-alls regarding the 37… you simply cannot easily drop a shell into the chamber. Also, being so lightweight, they tend to heat up real fast with any amount of shooting. You'll never hurt the gun this way, but don't burn yourself. Lastly, also a lightweight "thing" ...they kick! Most of the older guns only had a butt-plate ...and they're lightweight. The pop pretty good where some shooters prefer a heavier 12ga 870 to a 20ga Ithaca.
In buying these awesome ole shotguns a couple things to look for... if it's a pre '63 gun, do make sure the barrel and receiver serial number match, its just a lot easier this way. The guns are extraordinary well built with high quality steel, but in order to be so lightweight the steel can be a bit on the "thin" side in places like the barrel. If the barrel has any significant pitting, pass on it. Its usually not worth the hassle. Also, the wood in the wrist are of the stock cracks on a lot of guns, again, unless its an extraordinary acquisition, if the wood is cracked beyond what you can repair or want to pay to have worked on, pass. Factory Ithaca stocks can be tough to come by and
when you find them, they're usually pretty spendy.
With that said, go forth and find wonderful old Ithaca 37s at inexpensive prices.
...and because its arf.com and we need pics (OP, no pics?) ...a few of my beloved 37s
L to R: 1940 vintage trench gun/project, 1941 riot gun, 1943 riot gun, 1956 16ga, 1961 20ga, 1969 vintage factory trench gun, 1970 riot gun and 1971 riot gun. There are a few others that didn’t make the pic, but y’all get the general idea.
Of note, the 1971 gun on the far right has a factory SKT (skeet) choked barrel, first time I'd ever even heard of that.
Ithaca did make a number of "riot guns" with 20-inch FULL choked barrels intended for and marketed to corrections type folk.
The older guns from the 40s had the serial number stamped in the face of the wrist area of the stock.
Here are a couple that don't match from 1942. This is one of those unicorns McGavin mentioned above; WWII Ithaca M37 trench gun. There were 1422 made (1420 went out into the field and two went to a couple different ordnance officers for "inspections" and whatnot). After the war the military only "supported" the Winchester Model 12 and Stevens 520 and 620. Who knows what happened to those 1422 shotguns, but they are supposed to be the pinnacle of a collection along with the WWI Remington Model 10 trench gun.
Apologize for the long rant, I just get all kinds of excited about shotguns, Ithacas in particular. Hope it helps someone.