Many books have been published on the various models. Try Blue Book of Gun Values.
Try Browning or egunparts
There was no B letter prefix assigned to the browning auto-5 shotgun serial number range.Please look again and list the complete serial number and any letters that appear before,during,and after the serial number.
I have no records of a Browning 16ga shotgun having a A prefix to the serial number.Please check and list the model number(or name model) of your shotgun in your next post.
Gunbroker
list the serial number and we can help
The browning web page does not list serials this low and or numbers with a X. Based on that list it was made in the 30's?
You should be able to find a list of gun shops in your area that may have a Browning shotgun of this make.If you do not,I would go to gun broker.com.I believe that they will list a few of this model from time to time.
Look at the serial number again as this is imcomplete. Go to Browning's site, Support, Date your firearm and they have a list of dates.
.243 was made in a variety of Browning Rifle models. There are too many to list. Perhaps you could provide a model and we could tell you if it "wasn't" chambered in .243
Gun shops,craigs list,Gunbroker.com,Guns America etc.
The sn you list dates to 1978.
What shotgun?You need to list the maker of the shotgun,model number if there,type of shotgun(single shot,pump,semi-auto,over under,side by side.)gauge of shotgun(410,28,20,16,12)so that we can help you.