Will be date stamped for month/year check here: http://remingtonsociety.com/rsa/questions/barrelcodes
They only made them from 1936-1939, that's probably a first or second year production.
1920
I checked www.oldguns.net and they show the manufacture date of Remington 1903A3 serial no. 3851292 as 1942.
RW isn't part of the serial no, it stands for Remington Works 1915
That is not a serial no of a Remington 1911A1 they stopped in 1945 with 2465139.
1914
1913
1920
1919
late 1919
1920
1915
1912