"Perhaps it is unnecessary to be so explicit about it, but there are a lot of 16-byte addresses. Specifically, there are 2^128 of them, which is approximately 3 x 10^38. If the entire earth, land and water, were covered with computers, IPv6 would allow 7 x 10^23 IP addresses per square meter. Students of chemistry will notice that this number is larger than Avogadro's number. While it was not the intention to give every molecule on the surface of the earth its own IP address, we are not that far off."
-- Andrew S. Tanenbaum, talking about IPv6 in his book "Computer Networks."