My Router's WAN IP is a public IP - 172.100.x.x And my public IP is - 182.x.x.x
Why do I have 2 public IP's? Does this probably mean that my router is behind another router? But then what is the use of configuring 2 public IP's?
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I can see two possible explanations:
Your WAN address is your public address, but you are yourself using something that makes it look like you are accessing the internet somewhere else. One example is a proxy server which uses the 182-address to access the internet. A website telling you what your public IP is would see the 182 address. Often these sites will also tell you there is a proxy in play if the proxy sets the HTTP X-Forwarded-For header. Another possibility is a (VPN-)tunnel.
Your router is indeed behind another router performing address translation. Chances are your internet provider is doing carrier-grade nat. As to 'why?', ISPs do this to overcome an IPv4 address shortage. This way, they can provide internet access to many customers using just one public IP.
Assuming you are not using a proxy, something's off... It is indeed strange that a 172.100 address is being assigned to customers, which are then hidden behind some 182 network. 172.100 was assigned by ARIN, 182 by APNIC...
Assigning RFC1918 private addresses to customers when using carrier-grade NAT can cause problems when the same network is in use inside the customer's network. The right thing to do (according to RFC6598) would be using addresses from 100.64.0.0/10. Using (parts of) 172.100 avoids possible conflicts with private addresses, but could make (parts of) the hosts rightfully using 172.100 addresses unreachable for you. Also, using 172.100 creates a risk of these routes being leaked into the global BGP table.
This is speculation, but since your WAN IP starts with 172, someone could be assuming the whole 18.104.22.168/8 range is private (but actually only 172.16.0.0/12 is private). Otherwise, someone is knowingly squatting IP space.