In this particular case and speaking about WordPress 2.2.3, the (bunchofcharacters) is the MD5 sum of the site url minus any trailing slash.
Example: Let my site url be
https://localhost/wordpress/
Omitting the trailing slash and having this site
compute the md5 hash value will result in
bbfa5b726c6b7a9cf3cda9370be3ee91
which is precisely the (bunchofcharacters) found in the cookie.
I think the value suitable for reproduction is stored in the database table wp_options. Look for the value “siteurl” within the column option_name.
