Alternate timeline
(covers information from an alternate timeline)

In an alternate timeline, the USS Yellowstone was a 24th century Federation Yellowstone-class runabout operated by Starfleet. She was the prototype for her class.

In this timeline, Harry Kim helped design this vessel after graduating from Starfleet Academy in 2372, instead of joining the USS Voyager crew. The Yellowstone carried an experimental tetryon plasma warp drive. The prototype was destroyed later that same year, after Kim and Tom Paris stole it in a bid to restore the normal timeline. (VOY: "Non Sequitur")

Since the ship was partly designed by Kim when normally he would have been on Voyager, it is unlikely the vessel exists in the normal timeline.
According to the Star Trek Encyclopedia (4th ed., vol. 2, p. 335), the registry number of the Yellowstone was NX-74751. The runabout seen in the schematic for the class was a dorsal and port drawing of the USS Rio Grande.
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