You can also try:
INSERT IGNORE
INTO table_1
SELECT *
FROM table_2
;
which allows those rows in table_1 to supersede those in table_2 that have a matching primary key, while still inserting rows with new primary keys.
Alternatively,
REPLACE
INTO table_1
SELECT *
FROM table_2
;
will update those rows already in table_1 with the corresponding row from table_2, while inserting rows with new primary keys.