Rolex Oyster ref. 6426 without the word PRECISION

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Hello,

I stumbled upon this piece and was wondering if it is legit. The only concern I have is it does not contain the word PRECISION above the 6. Did Rolex really had a production run for this model? A quick check on the serial number reveals it was manufactured in 1963.
 
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It says 6426 on the case, and 6427 on the case back, fwiw.
Yes it is weird to me as well. What could be the possible reason behind the discrepancy?