What do you mean there's nothing special about it? It was your Dad's! Now it's yours to care for, for your Son. You'll find it handy, sweet shooting and plenty powerful for most game. Enjoy.

'Tx63s80' - Welcome to the KCA Forum. It's pretty neat you inherited a Family Hunting Krag!

Model 1899 carbine, #361842, would have been assembled at Springfield Armory, around December, 1901.

Your stock appears to be a 'cut-down' rifle stock, so it is not original to the carbine barreled-action.

Your hand-guard appears to be cut for the 1902 rear sight. This is a very useful rear-sight, if you want to add one to your Dad's Krag. They sell for about $70 on ebay, sometimes including the screws.
Reproduction sight-screws are available from S&S Firearms, (Glendale, N.Y.).

Your receiver appears drilled & tapped for a Weaver side-mount. The #2 adapter-plate (with screws) is pretty inexpensive, when one shows up on ebay. The #2 plate would cover-up some 'blemishes'.
The Weaver #49350, detachable 'one inch' Side-Mount, (which holds the scope and attaches to the #2 plate), is still available from some dealers for $40, or less.

You have a good Krag for Hunting and Plinking. Enjoy it as your Dad did!

Attached: Photo of 1902 sight and hand-guard. Photo of Weaver side-mount and adapter-plate for Krag. 

Cat Man is correct about the damage to the last digit.

Lots of model 1899 carbines around #361842, but also, the occasional model 1898 rifle.

It is all academic, when it is a 'drilled & tapped' Krag and not a candidate for restoration.

Nuts, I was hoping you had a carbine with a lots of parts worth a bazillion.
The carbine configuration is very handy and number of members have been sprucing up or building faux carbines from parts. No intention to defraud anyone, a faux carbine looks so nice if done well and yours has that look. Family heirloom and useful if you have an excuse to go hunting. 

IMHO - Model date does not influence value, if a Krag receiver has been drilled & tapped.

Model 1898 and model 1899 receivers are identical, except for the date.
Model 1899 receivers were intended to be carbines. Some carbines exist with receivers marked 1898 over-stamped 1899.

Some rifles exist with model 1899 marked receivers; there is uncertainty about the manufacture, (why, when, or who).

Measuring your barrel length from muzzle/crown to closed bolt-face, exactly, with a cleaning rod is a good clue to possible origin. A carbine barrel will be exactly 22 inches.

If a short barrel is even a fraction longer than 22 inches, it is a "cut-down" rifle barrel.

If I understand correctly, "Blocks" is a reference to the occasional periods, when Armory production was devoted to manufacturing a batch of carbines.

Krags were not manufactured in numerical order. Finished/numbered receivers went into parts bins to be randomly pulled for assembly.
Model 1898 and model 1899 serial numbers can intermix to some extent.
(Likely, the model-date 'stamp' was put on at a different time then serial number 'stamp').

Rifle stocks were not used to make model 1899 carbine stocks near the end of production.

In the mid-1920's, Benicia Arsenal was shortening Krag rifles for NRA member sales. These were cut to carbine length, put in a carbine stock, and fitted with 1903 Springfield front-sights. When the supply of carbine stocks was exhausted, rifle stocks cut to carbine length, were utilized. (BTW - I don't think your Krag is one of these "NRA/DCM carbines).