Its domain has a very high link authority/trust.

Back links, internal links, high number of indexed pages, domain age.. although I do wonder if they still rank as GOOD as they did a few years back. How many people have had troubles beating out a wiki recently?

96.6% of Wikipedia Pages Rank in Google’s Top 10

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Well Nancy12,
It couldn't hurt to try and emulate what they do could it....?
Site structure, internal and external links

Copy what the high ranked sites are doing and of course start getting backlinks.

GO FOR IT...!

I've been stuck behind wikipedia for over a year on an exact match .com. Need more quality links...

The reason is high quality content.The content on wikipedia is unique and very useful as a result it serves as a link bait in most of the cases.The content links of wikipedia are really strong and it gets them an added advantage.Hence wikipedia pages gets ranked soon.

Think about it this way for a minute - forget SEO; domain authority; backlinks; trust; site structure; etc. ...

If you were searching for information on a topic, more often then not, you can end up on a Wikipedia page. When you do, don't you think that the information on the topic is generally and usually quite good and helpful? .... then haven't Google done a good job in returning such a useful site so high in the search results?

Everybody links to wikipedia and it's a pretty good source