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the number of humans to have existed grows exponentially.
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This was exactly what I was going to point out. You are assuming linear growth of the total human population, or an even distrution of humans over time, this is severely flawed. Though it is not quite exponential over the complete history of man, it is definitely not linear.
Here's a really interesting website about population growth that can give you more accurate numbers to use:
http://www.prb.org/Content/Navigatio...ion_Growth.htm