32-bit unsigned integers are IPv4 addresses. Meanwhile, the IPAddress.Address property, while deprecated, is an Int64 that returns the unsigned 32-bit value of the IPv4 address (the catch is, it's in network byte order, so you need to swap it around).

For example, my local google.com is at 64.233.187.99. That's equivalent to:

64*2^24 + 233*2^16 + 187*2^8 + 99
= 1089059683

And indeed, http://1089059683/ works as expected (at least in Windows, tested with IE, Firefox and Chrome; doesn't work on iPhone though).

Here's a test program to show both conversions, including the network/host byte swapping:

using System;
using System.Net;

class App
{
    static long ToInt(string addr)
    {
        // careful of sign extension: convert to uint first;
        // unsigned NetworkToHostOrder ought to be provided.
        return (long) (uint) IPAddress.NetworkToHostOrder(
             (int) IPAddress.Parse(addr).Address);
    }

    static string ToAddr(long address)
    {
        return IPAddress.Parse(address.ToString()).ToString();
        // This also works:
        // return new IPAddress((uint) IPAddress.HostToNetworkOrder(
        //    (int) address)).ToString();
    }

    static void Main()
    {
        Console.WriteLine(ToInt("64.233.187.99"));
        Console.WriteLine(ToAddr(1089059683));
    }
}