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The phrase "a unique number" is correct and usable in written English.
It can be used when referring to a number that is one of a kind or distinct from others, often in contexts like mathematics, identification, or data analysis.
Example: "Each participant in the study was assigned a unique number to ensure anonymity."
Alternatives: "an individual number" or "a distinct number".
Exact(60)
From that point on, each statuette bears a unique number".
Assigning a test a unique number could allow it to be tracked from start to finish.
Each dendritic segment and unconnected spine fragment was given a unique number.
A bluenumber is a unique number that identifies people, organisations, places, and things.
Each card was embedded with a unique number that registered with the phone company whenever it was used.
Hereafter, each DPVA is assigned a unique number to distinguish from others.
The programmer is responsible for assigning a unique number to each label in each program (or subprogram).
Use only if the item being uploaded to eCommons has been assigned a unique number by another entity.
This paper proposes a general procedure to design a specific size DPVA for producing a unique number of configurations.
Your IP address is not captured, but a cookie with a unique number is set on your browser when you start using it, which persists into the future.
It means, for instance, that my bank account number and sort code become a unique number, which is then accessed by individual banks.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com