... was probably the world's first national park when it was opened in 1872. Wikipedia is cautious however, describing it as "widely held to be the first national park in the world."
It was also the USA's biggest, until 1980 when six bigger ones (all in Alaska) were opened. A seventh was opened in 1994: Death Valley (California and Nevada), making Yellowtone the eighth biggest.
The USA's biggest national park is now Wrangell–St. Elias National Park and Preserve. (Wrangell and St. Elias are the names of two mountain ranges in Alaska.)
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