There are not many records available to identify a canoe with a serial number in the 2000 range. The existing Old Town serial number records are missing between numbers 2442 and 2477. The existing Carleton serial number records are missing between numbers 2235 and 5481. The Kennebec serial number 2459 went on a Kineo model that was 18 feet long. The Old Town serial number 152459 went on an Otca model that was 17 feet long.
You may be able to identify your canoe from other characteristics described at http://www.dragonflycanoe.com/id/ in the Wood Canoe Identification Guide. It would also be helpful if you could post some pictures here along with the length and a few more details about your canoe.
There could be some additional serial number digits that are hidden. You may want to try a flashlight at a very low angle to emphasize the shadows or a crayon with paper like a grave stone rubbing. Feel free to reply here if you find anything more or have other questions.