That could be a correct serial. Each time they changed the prefix (K, 1K, 2K, etc) they started over at 1 or maybe 1000. AFAIK the 15-3 was only made in 2" and 4" barrel lengths between 1967-77. The later versions of the 15 (15-5 to be specific) were offered in longer barrel lengths (replacing the discontinued M14) but not the -3. The barrel pin was dropped in 1982 during the 15-4 run, so some are seen with it and some are seen without it.
This one is 11K3794 (note the number of digits) shipped in 1977. Just realized it's a last year production for the 15-3. Of course I added the polished stags, not original.