MySQL has a SQL query "SHOW INDEX FROM" which returns the indexes from a table.
For eg. - the following query will show all the indexes for the products table:-
SHOW INDEXES FROM products \G
It returns a table with type, column_name, Key_name, etc. and displays output with all indexes and primary keys as - 
*************************** 1. row ***************************
        Table: products
   Non_unique: 0
     Key_name: PRIMARY
 Seq_in_index: 1
  Column_name: product_id
    Collation: A
  Cardinality: 0
     Sub_part: NULL
       Packed: NULL
         Null: 
   Index_type: BTREE
      Comment: 
Index_comment: 
To just display primary key from the table use :- 
SHOW INDEXES FROM table_name WHERE Key_name = 'PRIMARY'