www3.is a common convention and nothing more. There is nothing in the HTTP specification that says a website must start with
www.or any other prefix. It is simply a convention that began in the early days of the web and was used to distinguish a company's web server from its FTP server, gopher server, mail server, et cetera. But no such distinction is necessary, because web servers respond on TCP port 80, which is distinct from port 25 (outgoing mail), port 110 (POP mail), port 21 (FTP control), et cetera. A single domain name can host all of these services, and a single physical computer may actually respond to many different domain names.
As a matter of common practice, most webmasters make sure their
sites respond to both
mycompanyname.com, because the former is the first
guess many people will make, and the latter is both more convenient
to type and easier to fit into an advertising logo. It is rare
for a well-run website to reject either name.
Some websites use
www4., etc. as names for additional web servers that
handle some of the traffic for the site. But it's strictly up to the
webmaster and the person who handles DNS for the domain. These could
just as easily be
dirtnap.example.com or whatever else.
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