500 ft in rural areas that still have buildings and structures of some sort, but FAA regs for private pilots state,"may fly at less than 500 feet when over “sparsely populated areas,” as long as the aircraft is not operated closer than 500 feet to any person, vehicle, or structure." Many parts of Wyoming would be considered to be "sparsely populated".
Check out 14 CFR 91.119 [1]. Over sparsely populated areas, there is no specific minimum altitude requirement—only that you need enough altitude to safely land following engine failure.