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If I have a password protected page, can the search engine still index it?
it just depending upon strength and authorities of your page !
and is Sitemap is active or not !
just a Like Example is SenukeX Forums is if you will go on Forums then it will ask for Password but if you will checkout any thread using Google Cache then you can check it fully and it shows login by GoogleBot
It may be but i am not sure..
no it doesn't mean unless you have a code in your html that restricts the search engine robot not to visit the page,that is when it will not visit the page
Yes Password Protected page may not index
If you have a password protected page, nobody including people and search engines can access that page. If search engines cannot access that page, they cannot crawl and index it. Having a sitemap wont help get that page indexed either if its password protected! You should password protect a page if you a) don't want anyone who doesn't have the password to gain access to it and b) you don't want Google to index that page. Password protected WordPress pages are not like forums which require login to access them. Google bot can create an account and then gain access to it which is why it would show in the search results or cached page results. But a password protected WordPress page Google bot cannot get the password for it and hence, cannot crawl and index it.
I think the crawlers of search engines do not need the password or anything because they are equipped with the facility to see parts of the web page. I don’t think the crawler will be seeing the entire web page because it is time-consuming and crawlers have a lot of work to do. From what I understand the site will be checked for the items that the search engine needs like the title, size of the content, tags (keywords) and the date of posting.