A 32-bit unsigned int has a range from 0 to 4,294,967,295. 0 to 65535 would be a 16-bit unsigned.
An unsigned long long (and, on a 64-bit implementation, possibly also ulong and possibly uint as well) have a range (at least) from 0 to 18,446,744,073,709,551,615 (264-1). In theory it could be greater than that, but at least for now that's rare to nonexistent.