primary key should always be unsigned?

since a primary key (identifier) wont be under 0, i guess it should always be unsigned?

TL/DR: Yes, but it almost doesn't matter.

Auto-increment always increases, so it will never use negative values. You might as well make it unsigned, and you get twice the range of values.

On the other hand, if your table uses 2³¹ values, it will probably also use 2³² values in a short time, so having twice the range of values isn't a big difference. You will have to upgrade to BIGINT anyway.

MySQL supports an optional SERIAL data type (presumably for compatibility with PostgreSQL, since SERIAL is not standard ANSI SQL). This data type is just shorthand that creates a BIGINT UNSIGNED.

Go ahead try it:

CREATE TABLE test.foo (foo_id SERIAL PRIMARY KEY);

SHOW CREATE TABLE test.foo;

CREATE TABLE `test`.`foo` (
  `foo_id` bigint(20) unsigned NOT NULL AUTO_INCREMENT,
  PRIMARY KEY (`foo_id`),
  UNIQUE KEY `foo_id` (`foo_id`)
) ENGINE=InnoDB DEFAULT CHARSET=latin1 

You get the same number of distinct values whether you declare an integer signed or unsigned: 2³² for an INT and 2⁶⁴ for a BIGINT. If the number is unsigned, you get values from 0 to that max value minus one. If the number is signed, you get values from -max/2 to max/2-1. Either way, you get the same absolute number of distinct values.

But since AUTO_INCREMENT starts at zero by default and increments in the positive direction, it's more convenient to utilize the positive values than the negative values.

But it hardly matters that you get 2X as many positive values. Any table that would exceed the maximum signed integer value 2³¹-1 is likely to continue to grow, so you should just use a BIGINT for these tables.

You're really, really, really unlikely to allocate more than 2⁶³-1 primary key values, even if you delete all your rows and re-load them many times a day.

Why exactly are you presuming that a primary key won't be under 0? That is not a given. I think you are confusing it with an identity column.

In any case it should make no appreciable difference either way, map the data type to the type of data you expect in the column regardless of whether it is a primary key or not.