Anyone know what these numbers are inside my case back please?

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Could be the movement number? Rolex watches have a serial numer (between the lugs) and also a different movement number engraved on the base plate:

Hi.
I will have a look at that.
Cheers, Michael
 
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I'm absolutely not into RLX, but I don't think so.

I have seen other diamond dialed watches with just "16000" inside the caseback.

But it looks like the caseback has been polished/brushed inside. The factory stampings don't seem so sharp and crisp as usual, while the digits must have been engraved later.

My 2c...

My photo was at an angle, the engraving is crisp, here is another shot 馃憤
 
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Could be the movement number? Rolex watches have a serial numer (between the lugs) and also a different movement number engraved on the base plate:

Just checked, the movement number and the weird inner case number, they are not related, so still a bit of mystery.

Thank you everyone for the ideas and opinions 馃憤
 
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Just checked, the movement number and the weird inner case number, they are not related, so still a bit of mystery.

Thank you everyone for the ideas and opinions 馃憤
I'm not really sure then, I'm no Rolex expert but of the casebacks I've seen there usualy only the reference number
 
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I'm not really sure then, I'm no Rolex expert but of the casebacks I've seen there usualy only the reference number

Thanks for your help anyway, always worth a try.
All the best, Michael
 
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these are your lotto/power ball lucky numbers! 馃榾 note: my commission is 1.5% of your first million prize.

馃榾
 
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One thing that is important to note here, those surely look like Rolex/Tudor engravings with the factory font, and very well done.
 
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One could also consider the different spacings of the stampings, but I'm not experienced enough to tell what is right or wrong (meaning different, so regular tolerance or not...):

957355-cdbc27c9c22d7fd23c6116a3018c19d0.jpg

f706e66d2d878e3a82b02797069bfe4192d352e4.jpg

The numbers were not done at the same time. the sixes are not the same at all.
 
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Those are service numbers, you can find also some starting with USXXXX. I had a GMT with the same type of engraving.
 
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Sorry to dig up an old post but my Submariner has its sn engraved inside the case back. I have not got a clue why but it is not unique as I have seen sn's engraved inside other Rolex case backs. It does seem to be very uncommon though. Could it be that your case back was intended for another watch. A simple mix up?
 
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but my Submariner has its sn engraved inside the case back.

Do you happen to have a photo?
 
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Serial numbers being engraved into casebacks is supposedly associated with 'special order' watches.

Obviously this doesn't explain why the serial in your caseback doesn't match the watch's serial, so possibly a mixup of some sort as @jaguar11 says, with a caseback originally intended for a special order watch being used instead for yours? It seems a bit far fetched, but is the most likely explanation in my opinion. Rolex were known to use whatever casebacks they had available rather than having a specific caseback for a specific midcase, hence your 16013 watch having a 16000 caseback and 5513s with 5512 casebacks etc.

Your watch's serial and the caseback 'serial' are also fairly close date-wise, with 'R' being the first letter prefix used following the use of number-only serials, so a low 9M serial is only around 1-2 years removed from an R serial.