23646 is what Longines calls an "order number" ("numero de commande") and it is not the Longines' internal reference number.
By contrast, and as Longines put it in an email to me a month ago, what's known as the "reference number" may appear on the inside case back but often does not appear on the case at all.
Bottom line, the Longines reference number is an internal reference which most often bears no connection to numbers engraved on the case-- and is separate from the "order numbers" on the case back.
From what I've seen on one of my watches, seems like the reference indicates the shape of the case and the caliber type (not the dial I was told). It therefore seems plausible (IMHO) that the order number on the outside of the case back refers to batches.