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The phrase "a separate number of" is correct and usable in written English.
It can be used when referring to a distinct quantity or count that is different from another number or group.
Example: "We need to account for a separate number of participants who registered late for the event."
Alternatives: "an additional count of" or "a distinct quantity of".
Exact(2)
In contrast, the disclosure did not offer a separate number of national security complaints, suggesting that some were not followed up with an assessment.
Superoxide dismutase was added to a separate number of experiments at a concentration of 20 μg/mL to investigate the requirement for superoxide in enzyme inactivation caused by hydrogen peroxide.
Similar(58)
In this paper the synthesis problem of distillation-based separation sequences that separate a number of multicomponent feed streams into a number of multicomponent products is addressed.
In order to separate a number of simultaneously active speech signals from recordings, with, the reverberant, noisy mixing process is modelled as (1).
The company had separated a number of their HR responsibilities to a number of different individuals.
Increasingly, all that separates a number of once-premier programs from the Manhattans of the country is reputation.
A separate sales number gave an estimate of a "47-minute" wait to speak to an advisor.
INM's largest shareholder, Denis O'Brien, controls a large slice of Ireland's newspaper industry and, through a separate company, a number of radio outlets.
A separate report the number of Americans signing up for state unemployment benefits last week rose unexpectedly to the highest level in more than four months.
Under a separate agreement, a number of Nato members - including Germany, Turkey, Italy - will contribute to a 12,000-strong force that will train and assist Afghanistan's security forces.
From Zhang's result, a deduction can be made, which is that there is a number smaller than seventy million which precisely defines a gap separating an infinite number of pairs of primes.
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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