Well, first of all the serial number given is for a model 37 and not the model 51. All model 51s serial number begin with 5100. Since your begins with 37 would you not believe that it is a model 37. Your model 37 was mfg circa 1975.
1987
Yes I have one and am loking for a deer barel for it.
I would buy one for about $250 $350
No such model exists. The Model 51 is a 22.
51 or so
I would try Numrich gun parts corp.they may be found on the web.
If it is in good shape it's probably worth between $250-$300. Look on www.gunbroker.com and see what they are selling for.
Browning never made a Model 51 shotgun.
Late 1926
65000 were made from 1917-1927 in 32ACP and 380ACP. http://unblinkingeye.com/Guns/Rem51/rem51.html
According to my records your model 12 was made in 1962 or 63. 1,900,000 were made between 1912 and 1963 for a total of 51 years production. Serial numbers started at 1 and ended with 1,900,000. More than likely yours was made in 1963. I hope this helped.