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Is it possible to have such date and day combination that doesn't occur on any year ever?

My friend told me a story yesterday and said "It happened on March 13th and it was Friday".

I was thinking about this and I've a question. Is it possible to have such date and day combination that it doesn't occur on any year ever?

For example, would it be possible to say that "March 13th" is never Friday (no matter which year). Or for example "Thursday, April 3", etc.

Is there such date that doesn't occur on any year no matter what year (future or past)?