A number this large

Mathematically, IPv4 can only support about 232 or 4.3 billion connections. IPv6, on the other hand, can handle 2128 or 34O,282,366,92O,938,463,463,374,6O7,431,768,211,456, connections.

The implications of a number this large are mind-boggling. There are only 1019 grains of sand on all the beaches of the world. That means IPv6 would allow each grain of sand to have a trillion IP addresses. In fact, there are so many possible with IPv6 that every single atom on our planet could receive a unique address and we would ‘still have enough addresses left to do another 100+ earths.’
Future Crimes, Mark Goodman, page 286. Interior quote is from Steve Liebson, “IPV6: How Many IP Addresses Can Dance on the Head of a Pin,” EDN Network, March 28, 2008; “The Internet of Things”.