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The phrase "number of existing" is correct and usable in written English.
It is used to describe the total or amount of something that exists at a particular time or up until a certain point in time. For example: The number of existing businesses in the area has increased by 5% over the past year.
Exact(59)
Mars also has a number of existing smallholder programmes.
Start with any number of existing programs that randomly generate music.
Procter and NBC signed up a number of existing organizations to supply content to Petside.
Trait data were obtained from a number of existing data sources listed in the Methods.
And third, a significant number of existing firearms are configured for 12- to 19-round magazines.
The number of existing homes sold in 2016 was a 10-year record.
Practical exercises cover how to use the book with a number of existing constraint languages.
There are a number of existing techniques for triggering the vaporization, each with inherent drawbacks.
Restricting our researchers to 60 or any other number of existing stem cell lines is beyond comprehension.
The ACCC also found evidence that a large number of existing gas pipeline operators had been engaging in monopoly pricing.
Applicants who want to get in on looks must subject themselves to a vote by a number of existing users.
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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