Mysql: find tables with no primary key

 SELECT t.table_schema,
       t.table_name,
       k.constraint_name,
       k.column_name
FROM information_schema.tables t
     LEFT JOIN information_schema.key_column_usage k
          ON t.table_schema = k.table_schema
             AND t.table_name = k.table_name
             AND k.constraint_name = 'PRIMARY'
 WHERE t.table_schema NOT IN ( 'mysql', 'information_schema',
                                       'performance_schema' )
       AND k.constraint_name IS NULL
       AND t.table_type = 'BASE TABLE'
       order by table_schema desc;