Although a nice piece it is not factory original and very, very, few are. Think of these old military rifles like an army jeep. When the axle goes bad, they put a new one in, same goes for other major components. These rifles were rebuilt numerous times at arsenals and depots where they were completely disassembled, all the parts separated and inspected and if found satisfactory, reassembled into complete rifles. Ammunition until the 1950's was corrosive so finding a good 10-12 is a real find. If the barrel and receiver are original to each other it's worth a good bit to a collector. Here is one collector's guide where he has documented original rifles and found serial numbers in armory documents.
Who knows what has been changed on your rifle since it left the military, but assuming it's as it was in service, the "RAP" stamp means it was rebuilt at Raritan Arsenal and P for proof fired. The stock the rifle came with was JFC and only had the rear stock reinforcing bolt. Originally your rifle was blued. Parkerizing was done when they were rebuilt.
Springfield Armory rifles under 800,000, some say 810,000 just to be safe, an exact serial number is not known are called low numbers by collectors today. The receiver was hardened by a single heat treat process that left the outside very, very hard but the inside soft. At least it was supposed to. Errors were made in the hardening process as the foundry workers eyeballed the correct temperature. This led to a number of these receivers being hard all the way through, sometimes called burned. The bad ones can shatter like glass from an overpressure event. The events that were documented back in the day were from bad ammo with brittle brass resulting in case head seperations and one was some idiot fired an 8mm mauser round! There have been no kabooms documented from good ammo. There is no way to tell without destroying the receiver if yours has a brittle receiver or not so the decision to fire it is yours. Once the problem was found, Springfield changed to a double heat treat process around 800,000 and finally a nickel steel receiver. The Army did not recall the low number rifles, they said when they come in for rebuilding, scrap the receiver, replacing it with a new one then getting the rebuid stamp. Your rifle could not have had the RAP stock installed at Raritan Arsenal, an Army facility, because they would have scrapped the receiver. The Marines, never having a lot of cash, fought on with the low numbers but as an extra measure of safety drilled a gas escape hole on the left side of the receiver ring known as a Hatcher hole. Later 03A3's had the hole from the factory.
The crack behind the trigger guard may be a problem. You need to remove the action from the stock. To do this remove the screw on the front band / bayonet lug, then loosen the lower band (this is the one with the sling swivel). Now depress the band spring on the right side of the stock and slide both the handguard and the lower band toward the muzzle together. Next take the screws out of the triggerguard. Inspect the wood where the front stock bolt passed through. This is the recoil lug, it is where all the recoil is supposed to bear. Sometimes this wood gets broken or battered back and the recoil is then taken up by the bushing the rear triggerguard screw passes through, eventually breaking the stock. It will have miserable accuracy too. New stocks are available from the CMP at a very reasonable price.
Now you can make an informed decision whether to fire it or not.