Is there a way to prevent requester notification if a request is created with a "Closed" status?

Is there a way to prevent requester notification if a request is created with a "Closed" status?

Many requests we create never have an "Open" status; they are merely created for posterity and reference with the status of "Closed." Upon creation with the "Closed" status, our requester immediately receives two emails--the first informing that a request has been created, and the second notifying that their request has been closed.  Is there a way to prevent any notifications being sent to a requester if the request is created with a "Closed" status?

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