-- Nullable column doesn't cause automatic primary key

MariaDB [mw]> create table t1 (a int);
Query OK, 0 rows affected (0.02 sec)
MariaDB [mw]> create unique index t1a on t1 (a); 
Query OK, 0 rows affected (0.06 sec)
MariaDB [mw]> select * from information_schema.innodb_sys_indexes, information_schema.innodb_sys_tables where innodb_sys_tables.table_id=innodb_sys_indexes.table_id and innodb_sys_tables.name='t1';
+----------+-----------------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
| INDEX_ID | NAME            | TABLE_ID | TYPE | N_FIELDS | PAGE_NO | SPACE | TABLE_ID | SCHEMA | NAME | FLAG | N_COLS | SPACE |
+----------+-----------------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
|   225970 | GEN_CLUST_INDEX |   103685 |    1 |        0 |    2154 |     0 |   103685 | mw     | t1   |    1 |      4 |     0 |
|   225971 | t1a             |   103685 |    2 |        1 |    2155 |     0 |   103685 | mw     | t1   |    1 |      4 |     0 |
+----------+-----------------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+

-- Other tests which do create primary keys:

MariaDB [mw]> create table t2 (a int not null);
Query OK, 0 rows affected (0.02 sec)
MariaDB [mw]> create unique index t2a on t2 (a); 
Query OK, 0 rows affected (0.05 sec)
Records: 0  Duplicates: 0  Warnings: 0
MariaDB [mw]> select * from information_schema.innodb_sys_indexes, information_schema.innodb_sys_tables where innodb_sys_tables.table_id=innodb_sys_indexes.table_id and innodb_sys_tables.name='t2';
+----------+------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
| INDEX_ID | NAME | TABLE_ID | TYPE | N_FIELDS | PAGE_NO | SPACE | TABLE_ID | SCHEMA | NAME | FLAG | N_COLS | SPACE |
+----------+------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
|   225973 | t2a  |   103687 |    3 |        1 |    2157 |     0 |   103687 | mw     | t2   |    1 |      4 |     0 |
+----------+------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
1 row in set (0.00 sec)

-- type=3 means primary key



MariaDB [mw]> create table t3 (a int not null, unique key (a));
Query OK, 0 rows affected (0.02 sec)

MariaDB [mw]> select * from information_schema.innodb_sys_indexes, information_schema.innodb_sys_tables where innodb_sys_tables.table_id=innodb_sys_indexes.table_id and innodb_sys_tables.name='t3';
+----------+------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
| INDEX_ID | NAME | TABLE_ID | TYPE | N_FIELDS | PAGE_NO | SPACE | TABLE_ID | SCHEMA | NAME | FLAG | N_COLS | SPACE |
+----------+------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
|   225974 | a    |   103688 |    3 |        1 |    2156 |     0 |   103688 | mw     | t3   |    1 |      4 |     0 |
+----------+------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+


-- Using PRIMARY KEY in CREATE TABLE generates an index which is the same except for its name

MariaDB [mw]> create table t4 (a int not null primary key);
Query OK, 0 rows affected (0.02 sec)

+----------+---------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
| INDEX_ID | NAME    | TABLE_ID | TYPE | N_FIELDS | PAGE_NO | SPACE | TABLE_ID | SCHEMA | NAME | FLAG | N_COLS | SPACE |
+----------+---------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+
|   225975 | PRIMARY |   103689 |    3 |        1 |    2158 |     0 |   103689 | mw     | t4   |    1 |      4 |     0 |
+----------+---------+----------+------+----------+---------+-------+----------+--------+------+------+--------+-------+