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The phrase "a special number" is correct and usable in written English.
You can use it when referring to a number that holds particular significance or uniqueness in a given context.
Example: "In mathematics, pi is often considered a special number due to its unique properties and appearance in various formulas."
Alternatives: "a unique number" or "a significant number".
Exact(42)
Quite a special number.
She had a special number.
"Twenty-three is a special number," he admitted.
That produced hundreds of phone calls to a special number, but no significant leads.
In 1927 a special number of the American Journal of Psychology honoured Washburn.
Under call-back systems, the overseas caller dials a special number, lets it ring once and hangs up.
Similar(18)
British ships, after the mutiny at the Nore (1797), followed a special numbering in the dogwatch.
Each artist will create a special numbered and signed edition of prints that will go on sale on 6 June, at art.tfl.gov.uk/shop/.
He's selling three titles including a special issue — number 3.14 — featuring geek strips.
Today, 14 March, is Pi Day, an annual celebration of a rather special number: pi.
You have to call a special 800 number to get a hold of him.
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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