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The phrase "a unique number for" is correct and usable in written English.
It can be used when referring to a specific identifier or code that is distinct and assigned to something, such as an account, item, or record.
Example: "Each customer is assigned a unique number for tracking their orders in our system."
Alternatives: "a distinct identifier for" or "a specific code for".
Exact(14)
The International Standard Music Number is a "unique number for the identification of all printed music publications... whether a part, a score, or an element in a multi-media kit" that became available at the end of 1993.
Unicode provides a unique number for every character.
DBLP resolves the author ambiguity issue by means of a unique number for each author.
A total of 319 individuals were enrolled, and each was attributed a unique number for this study.
To control for the use of the same individual multiple times, an individual's ID (a unique number for each individual) was added as random factor.
Each allele was designated a unique number for each locus, and a multilocus genotype (MLG) defined by the specific combination of alleles at all seven loci.
Similar(46)
The segments input file is a csv file separated by commas with the following columns: (1) segment id, which is an unique number for each row; (2) row number in the raw file where the segment starts; (3) row number in the raw file where the segment ends.
This paper proposes a general procedure to design a specific size DPVA for producing a unique number of configurations.
All contrasts bare a unique number, used for cross-referencing in the manuscript's text.
The experiment identification (id) is a unique number created for each new docking experiment with an FFR model and one ligand.
Veldkamp provided us with a unique number code for each respondent and did not link the answers to identifying information of the participants.
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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