select some_other_column
from `table`
order by primary_index_column asc
limit 4000000, 10;

select some_other_column
from `table`
order by secondary_index_column asc
limit 4000000, 10;

mysql> explain select some_other_column from `table` order by primary_index_column limit 4000000, 10;
+----+-------------+---------+-------+---------------+---------+---------+------+---------+-------+
| id | select_type | table   | type  | possible_keys | key     | key_len | ref  | rows    | Extra |
+----+-------------+---------+-------+---------------+---------+---------+------+---------+-------+
|  1 | SIMPLE      | table   | index | NULL          | PRIMARY | 4       | NULL | 4000010 |       |
+----+-------------+---------+-------+---------------+---------+---------+------+---------+-------+

mysql> explain select some_other_column from `table` order by secondary_index_column limit 4000000, 10;
+----+-------------+---------+------+---------------+------+---------+------+---------+----------------+
| id | select_type | table   | type | possible_keys | key  | key_len | ref  | rows    | Extra          |
+----+-------------+---------+------+---------------+------+---------+------+---------+----------------+
|  1 | SIMPLE      | table   | ALL  | NULL          | NULL | NULL    | NULL | 4642945 | Using filesort |
+----+-------------+---------+------+---------------+------+---------+------+---------+----------------+

ALTER TABLE `table` ADD INDEX mynewndx (indexed_column,some_other_column);