...careful with the serial numbers though, they didn't have the best heat treatment back then
Only an issue with WWI era 1903s - Springfield Armory below serial number 800,000 and Rock Island Arsenal below serial number 286,506. Not an issue with the WWII era Remington and Smith Corona 1903A3s.
Here's more on the heat treatment issue:
http://m1903.com/03rcvrfail/