Sometimes to clarify a worn or damaged number, usually in clumsy style and to greater harm than good.
Sometimes to disguise a stolen watch.
Sometimes simply to match a set of spare papers to a watch with none. The [perceived] added value of a watch with papers is far greater than the cost of the renumbering, to the unscrupulous.
If one has been renumbered, it is then often impossible to determine the original identity, whether the number is in fact correct or has been changed.
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