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That's the area I was thinking of as most remote (continental US) too. SE Oregon/SW Idaho. Owyhee County Idaho has a population density of only 1.4 / sq mile
According to the US Census Oregon has three counties with less than 1 person / sq. mile: Wheeler, Lake, and Harney.
Montana does have some low population areas, just like other states have.
Carter County,
Garfield County,
Golden Valley County,
McCone County,
Meagher County,
Petroleum County,
Phillips County,
Powder River County,
Prairie County,
and Treasure County.
If you want isolated and sparse population, try west Texas. Yes there are some good size cities, Lubbock, Amarillo, Midland, but once you get out of these cities, its 350 miles to Dallas, 400 to Austin, 300 to Abq. and well, there's nothing north of Amarillo to you get to Colo Springs and Denver, but that's also 400 miles. Some of the counties here only have 300 people and they are still shrinking.
Definitely consider Modoc County, California, in the far northeast corner of the state. Fewer than 10,000 people in the entire county, at just 2 people per square mile. Which is an average. Outside of Alturas it's probably more like 2 people per 50 square miles. Beautiful, beautiful country. Probably California's most conservative county both socially and politically. Beware the local politics, however. I've heard that local cattle ranching families have been feuding for generations, sometimes violently.
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