Well I was close
no, you were right - it's just that's how it
used to be. before you used to be able to walk into a cummins parts place and give them the CPL. now, they can't look anything up w/out the ser no. and most places will not sell you any parts unless it is "authorized" for that ser no.
at least, that's been my experience.
but, as stated, both numbers should be on a tag on the side of the front gear case, usually between the injector pump and accessory drive locations.