It is not the PN or the SKU. I just checked the back of my old spare x1950 pro and there is a third number on a separate sticker with a bar code above. Their RMA form says it is written on the back of the card (PCB) so that must be the number.
There is no indication on my card either that it is the serial but knowing that it is not the other two leaves me with only one option.
If you put in that number they will simply reject it if it is not the correct one and you get another try.