添加列之后，您始终可以添加主键:

After adding the column, you can always add the primary key:

ALTER TABLE goods ADD PRIMARY KEY(id)

关于为什么脚本无法正常工作，您需要指定PRIMARY KEY，而不仅仅是单词PRIMARY:

As to why your script wasn't working, you need to specify PRIMARY KEY, not just the word PRIMARY:

alter table goods add column `id` int(10) unsigned primary KEY AUTO_INCREMENT;