I am oddly interested in the list of the Longest-Running Broadway Shows. The Book of Mormon, which is still running at the Eugene O'Neill Theater back there, just surpassed 42nd Street to become #14 on the list.
The Book of Mormon is currently running at around 100% capacity so it'll almost surely be around to pass #13 (Miss Saigon) and maybe #12 (Jersey Boys). Beyond that, it's a big maybe.
It will definitely not grab the #1 spot from The Phantom of the Opera since The Phantom of the Opera is still running. And not only is it still running but it's playing to 95% capacity, which is way more than is necessary for a show that has already paid off all its opening expenses a hundred-plus times over. In fact, they just put a whole new marquee advertising it on the front of its theater.
If for some not-gonna-happen, science-fictiony reason Phantom of the Opera were to close tomorrow and so did all the other shows still open and competing for the top position (Chicago, The Lion King and Wicked), The Book of Mormon could conceivably grab the Number One spot. All it would have to do is to continue running until around Christmas of the year 2042.