Varchar or integer primary key?

I have a 6-digit integer number for a patient identifier which
I intend to use as a primary key (PK) for a table. It also will
be a foreign key in other tables. Do I have to use an integer data
type as a domain for this PK or could I use a varchar(6)?  Is there
any difference between an index on an integer column and one on a
varchar column?

I've been searching the internet and books for something to help on
this question but I haven't found. There are lot of good discussions on
choosing primary keys but nothing related to my issue.
Any suggestions or references may help.

Thanks in advance,
Rafael