It’s slow because it needs to locate the top offset rows and scan the next 100. No amounts of optimization will change that when you’re dealing with huge offsets.
This is because your query literally instruct the DB engine to visit lots of rows by using offset 3900000 — that’s 3.9M rows. Options to speed this up somewhat aren’t many.
Super-fast RAM, SSDs, etc. will help. But you’ll only gain by a constant factor in doing so, meaning it’s merely kicking the can down the road until you reach a larger enough offset.
Ensuring the table fits in memory, with plenty more to spare will likewise help by a larger constant factor — except the first time. But this may not be possible with a large enough table or index.
Ensuring you’re doing index-only scans will work to an extent. (See velis’ answer; it has a lot of merit.) The problem here is that, for all practical purposes, you can think of an index as a table storing a disk location and the indexed fields. (It’s more optimized than that, but it’s a reasonable first approximation.) With enough rows, you’ll still be running into problems with a larger enough offset.
Trying to store and maintain the precise position of the rows is bound to be an expensive approach too.(This is suggested by e.g. benjist.) While technically feasible, it suffers from limitations similar to those that stem from using MPTT with a tree structure: you’ll gain significantly on reads but will end up with excessive write times when a node is inserted, updated or removed in such a way that large chunks of the data needs to be updated alongside.
As is hopefully more clear, there isn’t any real magic bullet when you’re dealing with offsets this large. It’s often better to look at alternative approaches.
If you’re paginating based on the ID (or a date field, or any other indexable set of fields), a potential trick (used by blogspot, for instance) would be to make your query start at an arbitrary point in the index.
Put another way, instead of:
example.com?page_number=[huge]
Do something like:
example.com?page_following=[id]
That way, you keep a trace of where you are in your index, and the query becomes very fast because it can head straight to the correct starting point without plowing through a gazillion rows:
select * from foo where ID > [id] order by ID limit 100
Naturally, you lose the ability to jump to e.g. page 3000. But give this some honest thought: when was the last time you jumped to a huge page number on a site instead of going straight for its monthly archives or using its search box?
If you’re paginating but want to keep the page offset by any means, yet another approach is to forbid the use of larger page number. It’s not silly: it’s what Google is doing with search results. When running a search query, Google gives you an estimate number of results (you can get a reasonable number using explain), and then will allow you to brows the top few thousand results — nothing more. Among other things, they do so for performance reasons — precisely the one you’re running into.