Thanks sipa for this thorough answer.
Incidentally, I have read somewhere that there are approximately the same number of bitcoin addresses as there are atoms on earth.
Did anyone check that ?
I guess it depends on your definition of "approximately". There are actually about 70 times as many atoms in the Earth as there are bitcoin addresses:
Number of bitcoin addresses (2^160): 1.462 quindecillion
Number of atoms in the Earth (according to
Wolfram Alpha): 100 quindecillion