Air-King Date listed with incorrect reference

[Beenacho]

Hi all,

I came across an Air-King Date with linen dial for sale in a vintage watch store, however the reference was listed as 1500. From my research it looks like this watch should be a ref 5700, since the 1500 should be an Oyster Perpetual Date.

Is it possible that this watch has been fitted with an incorrect caseback? Is there any way to tell what the actual reference is (ie. is the reference stamped anywhere else on the watch?)

Thanks for your help.

Side question: are there any other comparable models I should look at? I've also been considering Datejust 1601/1600s.

[Tools]

The case reference is stamped on the side of the case, under the bracelet.

Some case backs do have stamps, but since so many are interchangeable it doesn't tell you much unless you know that it is an original back.