If you could post some pictures it would be a big help!! As Dick says the serial number is far out of the carbine range. But if cut to carbine length you should have a handy shooter/hunting rifle. It is amazing the amount of misinformation that is out there!! Stories get told a couple of times and suddenly they are gospel!!! :( So many official and "unofficial" changes were made over the years that pictures are usually needed if possible!!
There is a partial serial number list in the back of Mallory's book, I believe that Springfield Research Service has a slightly up dated list, but that info will cost you I think.
Enjoy your Krag!!!!!!!!!