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I've activated plugin but don`t see any numbers on my favicon

Make sure your favicon.ico is in your site's root directory (where wp-config.php usually is) and NOT in your theme`s folder.

I've got favicon in my root folder but still don't see numbers

Your favicon must be in .ICO format and not in .PNG or .GIF or any other.

Which browsers are supported?

The authors of the script [Notificon script] (https://github.com/makeable/Notificon) (the script this plugin is based on) claim to support Chrome 6+ and Firefox 2+ and Opera.