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We could check for Virginia counties less populous than Rappahannock. The U.S. Census Bureau’s Population Estimates Program notes seven such counties as of July 1, 1999.
If you want peace and quiet, away from people, move to Highland County. If you really want peace and quiet, try North Slope Borough (County) of Alaska.
It has 7,089 people in 87,861 square miles, for a population density of 0.08 people per square mile. That county is 329 times bigger than Rappahannock County. It is twice as large as Virginia.
This brings up an interesting point. Population density is calculated by dividing population by square miles. For Rappahannock County, the 1999 estimated population of 7,664 people divided by the county's area of 267 square miles gives 29 people per square mile.
You can picture this at Massie's Corner going west on Route 211. Starting at Massie’s Corner and looking up Route 522 to the foothills of Little Mulky Mountain is
96.9%