MySql - Is primary key unique by default?

Primary key is always unique in every SQL. You dont have to explicitly define it as UNIQUE.

On a side note: You can only have onePrimary key in a table and it never allows null values. Also you can have only one primary key constraint in the table(as the point of creating a primary key is to uniquely identify the row in your table) but you can more than one unique key constraint in your table.

Example:

An employee details table having EmpID as Primary key and EmpPhoneNo as unique key.

Primary key is always unique by definition. Not only in MySQL. So you don't need any additional unique key.