The 192.x.x.x address is private address space.
Private IP address space is defined in
RFC1918: Address Allocation for Private Internets.
The three address ranges reserved for private address space are:
10.0.0.0 - 10.255.255.255 (10/8 prefix)
172.16.0.0 - 172.31.255.255 (172.16/12 prefix)
192.168.0.0 - 192.168.255.255 (192.168/16 prefix)
These address spaces are special, in that they can be re-used over and over again by every private network. However, because of this, these address spaces are also unroutable.
The private IP addresses are the addresses used by everything on your side of the cable modem.
The 82.72.3.91 address is the public IP address issued to you by your ISP, AtHome. This IP address is used by the interface of the cable modem which is connected to the AtHome network.
AtHome probably uses
DHCP to issue these IP addresses. Their DHCP server most likely caches the
MAC address on your cable modem. Every time it sees that MAC address, it assigns the same IP address to it.
DHCP servers will only cache MAC addresses for so long. Therefore, if you turn off your cable modem, eventually the DHCP server will forget your MAC address and your old IP address. Then, when you turn your cable modem back on, the DHCP server will randomly assign you a new DHCP address. Unfortunately, there is no way for you to tell how long you would have to wait. I often set this timeout to eight days, but it could be set to almost anything.
Alternatively, you could replace your cable modem and it would have a different MAC address. The DHCP server would then randomly assign a new IP address to you.
Of course, you could randomly get your old IP address again.
