perl 
-nwle"/bn(\d{4})/ && $1 >= 4000 && $1 <=6200 && ++$c{ $1 };" 
-e"END{ print qq[$_ => $c{ $_ }] for sort keys %c}" temp.dat

4370 => 1
4512 => 1
5600 => 2
6042 => 1
6085 => 2