MySQL - UPDATE query with LIMIT

I want to update rows in my table with starting from 1001 to next 1000.

I tried with following query:

UPDATE `oltp_db`.`users` SET p_id = 3 LIMIT 1001, 1000

1. This is giving me syntax error. Is this correct? am I doing any mistake here.
2. Can we limit update in this way?

Also, the rows that I am trying to update are having Null value for the column p_id which is having data type INTEGER. Due to this I am not even able to update using following query:

UPDATE `oltp_db`.`users` SET p_id = 3 WHERE p_id = null

1. Is my above query correct?
2. What can be done to achieve this?

If you want to update multiple rows using limit in MySQL you can use this construct:

UPDATE table_name SET name='test'
WHERE id IN (
    SELECT id FROM (
        SELECT id FROM table_name 
        ORDER BY id ASC  
        LIMIT 0, 10
    ) tmp
)

When dealing with null, = does not match the null values. You can use IS NULL or IS NOT NULL

UPDATE `smartmeter_usage`.`users_reporting` 
SET panel_id = 3 WHERE panel_id IS NULL

LIMIT can be used with UPDATE but with the row count only

I would suggest a two step query

I'm assuming you have an autoincrementing primary key because you say your PK is (max+1) which sounds like the definition of an autioincrementing key.
I'm calling the PK id, substitute with whatever your PK is called.

1 - figure out the primary key number for column 1000.

SELECT @id:= id FROM smartmeter_usage LIMIT 1 OFFSET 1000

2 - update the table.

UPDATE smartmeter_usage.users_reporting SET panel_id = 3 
WHERE panel_id IS NULL AND id >= @id 
ORDER BY id 
LIMIT 1000

Please test to see if I didn't make an off-by-one error; you may need to add or subtract 1 somewhere.