Actually, a different way using a different SQL query (which I was hoping to avoid, since that's dependent on parsing specific output):

my $keys_ref = $dbh->selectall_arrayref("SHOW KEYS FROM $table");     
+             
    
foreach my $row ( @{$keys_ref} ) {
    print "Primary key: $row->[4]"
        if $row->[2] eq 'PRIMARY';
}
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It'd probably be more readable to use a selectall_hashref and (in the MySQL case) snag

$row->{'Column_name'} if $row->{'Key_name'} eq 'PRIMARY'
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Edited by Chady -- added code tags.