1932-1935 - see Remington Society link
Which model, what condition, condition, and condition?????
The Remington Model 41 was made from 1936-1939, they will have the date code stamped on the left side of the barrel. You can look up this code at the Remington Society of America, I will add a related link to this answer with it.
Model 581.
Are you sure of the model number?
Manufactured 1925
1919 depends entirely on condition $100-1,200
You will have to contact Remington.
They only made them from 1932-1935 and they are date code stamped on the barrel. See related links for information on the Remington Society of America.
Which model, what condition?
SN's were not required before 1968
1918