My external IP address appears to change automatically [duplicate]

Solution 1:

10.X.X.X is a Class A private network IP range. All values in here are always on a private network. Some routers utilize 192.168.X.X, a Class C private network IP range. You should always see one of these ranges as your "default gateway," unless you're directly connected to the internet. Most providers today are using NATs unless you request a static IP address. This means that your IP of 88.207.251.1 is probably shared with other "Entreprise des P&T" customers on your local node (possibly your neighborhood or city).

Using NAT allows service providers to provide many more customers service than they could using only their allocated IP addresses. Since the IPv4 space has been completely exhausted, such tricks are necessary to keep the Internet going while everyone upgrades to IPv6. Contact your service provider if you want a dedicated IP address, and expect to pay more for the service.