For performance reasons almost all database systems use an unique index to implement a primary key. So the key (pun intended) is to look for such an index. Both DB2 for Linux, UNIX, and Windows (LUW) and DB2 for z/OS store information about indexes in a system table SYSIBM.SYSINDEXES. On DB2 for z/OS that table is exposed to the user and documented here. DB2 LUW has catalog views on top and the view to use is named SYSCAT.INDEXES, however querying the table still works:
WHERE TBNAME = 'MYTABLE'
AND UNIQUERULE = 'P'
The query returns the columns on which the primary key is defined for the table MYTABLE. As can be seen in the documentation, the UNIQUERULE provides information about whether the index is an index with duplicates, an unique index, or it is used to implement a primary key (value P). On DB2 LUW we could write the query utilizing the catalog view SYSCAT.INDEXES. The following query returns the table name and schema as well as the column names for all tables which have a primary key defined:
SELECT TABNAME, TABSCHEMA,COLNAMES
So the key to quickly working with primary keys are indexes and their metadata...