Work out private vs public ip instantly with clear inputs, formula shown and shareable results.
RFC 1918 sets aside 10.0.0.0/8, 172.16.0.0/12 and 192.168.0.0/16 for private use; those addresses are filtered by internet routers and must be translated by NAT. Other blocks are special rather than private: 169.254.0.0/16 is link-local autoconfiguration, 127.0.0.0/8 is loopback, and 100.64.0.0/10 is carrier-grade NAT space that subscribers often mistake for public.
Range membership test
address is in block if (address AND mask(prefix)) equals the block's network address
No. Providers drop RFC 1918 sources and destinations, so traffic must be translated to a public address at the edge.
That is carrier-grade NAT. The provider is sharing public addresses across subscribers, so inbound port forwarding will not work without a public IP.