If it's a pump action...
And REALLY old a model 12 from 1912 otherwise it's a 121 from 1951.
All model 121's are marked so and there is a barrel date code but a model 12 wouldn't have either a model or a barrel code being that old. The model 12 forstock is rather short and bulges in the middle the 121 is much longer and straight.
Now if it's a bolt it could be a lot of things but I don't know them as well and off-hand I don't think they had any with octagon barrels. It is niether bolt or pump action. You have to pull the hammer all the way back then there is an additional hammer you have pull back and then you are able to load the shell. It is a single shot. That means it's likely a model 4 rolling block.
A model 4 can either a solid frame or a take down with a lever or a screw on the side and it would have been made in 1905. There's a model 6 but the take down screw is on the bottom but I don't think they made any with octagon barrel.
Your Remington model 1903-A3 was made in the year 1942.It was chambered in the caliber 30-06.
You will have to contact Remington.
1 in 10
List the caliber and then someone will try to help you.
Impossible to tell unless you have the factory records.
Model 581.
$500 up
1920
1918
Are you sure of the model number?
SN's were not required before 1968
If you mean the US Rifle, Caliber 30, Model of 1917, manufactured by Remington, these were produced only in 1917-1918.