There's a corner of Oregon where it's 1 per square mile:

http://en.wikipedia.org/wiki/Harney_County,_Oregon

Beautiful place in its own stark way - especially Steens Mountain. I wouldn't want to live there, though.

Well, I bet that there are corners of Wyoming that are that un-dense. Maybe most of the state outside of the I-80 strip?

Oh, I'm sure there are, I just think it's an interesting corner of Oregon that's worth pointing out because it's really unknown, but beautiful and fascinating.