3.23.51 LIMIT efficiency problem

[Mark Hazen]

I am using MySQL 3.23.51 on Linux.  I have a fixed-length table with 45
million rows.  It appears MySQL has an efficiency issue with the LIMIT
command.  When I run SELECT a FROM b LIMIT 0, 1000000   <-- that's one
million
The query finishes almost immediately.

But when I run 20 million rows into the dataset, it really slows down.
(pretend the commas aren't there)
SELECT a FROM b LIMIT 20,000,000, 1,000,000

Why would it slow down?  We're dealing with a fixed-length table here.  This
is just mathematics to figure out where row 20,000,000 is.

Confused,
Mark