Someone's claim to fame can be unexpected or trivial, not always prestigious or admirable. His claim to fame was being the loudest snorer in the hostel.
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Can Be Past
The phrase often refers to past achievements or records that no longer hold. Her claim to fame was winning a national chess championship as a child.
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Irony Usage
It can be used ironically to mock something that is not very impressive. His claim to fame is eating 50 hotdogs at once, if you can call that fame.