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Strictly speaking, if the population hit 314159265 million, that would be closer to 10^14 times pi.
You didn’t mean the “million” in your title. :-)
Imagine a U.S. with 314 trillion people. Our land area is 9 trillion square meters, so we’d have about 35 people per square meter. Of course, with skyscrapers plating the continent to 100 stories, we could assign nearly 3 square meters of living space to each and every person.
Ventilation might present a slight problem. I’m also wondering about how Congress could stay as organized and productive as it now is while reconciling the views of a few billion representatives.