I think only if the F is in the second set of numbers does it show that it came from a factory store. I have some from the factory store and it is in the second set of numbers and the bag like shown (but mine is black) the serial number starts with an F and it came from the store in the mall
PS Fakes are a little hard to spot...my cousin got one and swears its real and it has the serial numbers in it. I know it isnt because it came "new" w/plastic coverings on the handles and it came from a swap meet!