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We all know that G's site command is a useful tool to show how many pages our sites have listed in the index
Does the site: command show what pages G thinks are important on your site in the first positions?
we all know that it is broken. So very, very, very broken.
It would make life much easier for webmasters if the site: results were listed in page trust/quality.
The one thing you can sort of depend on is that the domain root should be #1 - if it isn't, something is wrong somewhere. But what that may be (your problem or Google's) is not always clear. The only thing that is clear to me is that it is not a healthy sign.
1. Where does the homepage rank?
2. Do the pages that rank ahead of it have a large quantity/quality of incoming links?
What exactly do you mean by "broken"?
...Google will return the blocked URLs (and how many of them there are) when you use the site:- operator