A primary key is not an index, though all database management systems of which I know implement unique indexes to enforce the primary key constraint. A composite primary key would therefore result in an index of multiple columns. As with all B-Tree style indexes, the columns of a composite index are ordered.
If you had an index of LAST_NAME, FIRST_NAME (primary key or not) in that order, and your query includes a where clause that states LAST_NAME = 'SMITH' and FIRST_NAME = 'JOHN', then the index would probably (almost definitely) be used. In the case that you only stated LAST_NAME = 'SMITH', the index would probably be used as well, as LAST_NAME is the first element in the composite index. If in the case you only used FIRST_NAME = 'JOHN' in the where clause, the index would most likely not be used. To answer your question, when using the first n elements of an index in a where clause, the DBMS will most likely use the index to retrieve the result set, even if not all the columns of the index are specified.
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This was first published in February 2003