If it's not in the
table, then, yeah, I'll just need the S/N prefix, since you already mentioned that's it's a White KT4 purchased in Europe

.
EDIT: That said, that W could be ambiguous (I usually assume it means WiFi only, but it gets trickier with models that have a white variant). Does it have LTE support?
EDITē: Except, no, the S/N has nothing to do with the Factory JB being successful or not, so, do answer that S/N question, but that smells like you're not really on a factory FW.