Why Index (on primary key column) is not used? - mysql

Question

I have a date table, which has a column date (PK). The CREATE script is here:
CREATE TABLE date_table (
date DATE
,year INT(4)
,month INT(2)
,day INT(2)
,month_pad VARCHAR(2)
,day_pad VARCHAR(2)
,month_name VARCHAR(10)
,year_month_index INT(6)
,year_month_hypname VARCHAR(7)
,year_month_name VARCHAR(15)
,week_day_index INT(1)
,day_name VARCHAR(9)
,week INT(2)
,week_interval VARCHAR(13)
,weekend_fl INT(1)
,quarter_num INT(1)
,quarter_num_pad VARCHAR(2)
,quarter_name VARCHAR(2)
,year_quarter_index INT(6)
,year_quarter_name VARCHAR(7)
,PRIMARY KEY (date)
);
Now I would like select rows from this table with dynamic values, using such as LAST_DAY() or DATE_SUB(DATE_FORMAT(SYSDATE(),'%Y-01-01'), INTERVAL X YEAR), etc.
When one of my queries failed and didn't execute in 30 secs, I knew something was fishy, and it looks like the reason is that the index on the primary key column is not used. Here are my results (sorry for using an image instead of copying the queries, but I thought it's concise enough for this purpose, and the queries are short/simple enough):
First of all, it's strange that the BETWEEN works differently than using >= and <=. Secondly, it looks like the index is only used for constant values. If you look closely, you can see that on the right side (where >= and <= is used), it shows ~9K rows, which is half of the rows in the table (the table has about ~18k rows, dates from 2000-01-01 to `2050-12-31).

Answer 1

SYSDATE() returns the time at which it executes. This differs from the behavior for NOW(), which returns a constant time that indicates the time at which the statement began to execute. (Within a stored function or trigger, NOW() returns the time at which the function or triggering statement began to execute.)
-- https://dev.mysql.com/doc/refman/5.7/en/date-and-time-functions.html#function_sysdate
That is, the Optimizer does not see this as a "constant". Otherwise, the Optimizer eagerly evaluates any "constant expressions", then tries to take advantage of knowing the value.
See also the sysdate_is_now option.
Bottom line: Don't use SYSDATE() for normal datetime usage; use NOW() or CURDATE().

Answer 2

Looks like if I use CURRENT_DATE() (or NOW()) instead of SYSDATE(), it's working. Both of these queries:
SELECT *
FROM date_table t
WHERE 1 = 1
AND t.ddate >= LAST_DAY(CURRENT_DATE()) AND t.ddate <= LAST_DAY(CURRENT_DATE());
SELECT *
FROM date_table t
WHERE 1 = 1
AND t.ddate >= LAST_DAY(NOW()) AND t.ddate <= LAST_DAY(NOW());
Give the same result, which is this:
I will accept my answer as a solution, but I'm still looking for an explanation. I thought it might has to do something with SYSDATE() not being a DATE, but NOW() is also not a DATE...
EDIT: Forgot to add, BETWEEN is also working as I see.