You had a bug in spr_f() (you end up using a format of "%06" instead of "%06d"). That didn't seem to affect the speed much, though. You also don't return the correct value from concat() so I fixed that too. I made spr_f() a bit faster by eliminating the extra copy. This penalizes concat() since it is now the only one that needs the extra copy (oh well).

I added my favorite (that I learned from chip) and reran the benchmark:

#!/usr/bin/perl -w

use strict;

use Benchmark qw( cmpthese );

my $num= 13;
my $wid= 6;

sub concat {
    my $a= $num;
    $a= "0$a"   while  length($a) < $wid;
    $a;
}

sub spr_f {
    sprintf( "%0${wid}d", $num );
}

sub sub_s {
    substr( "0"x$wid.$num, -$wid );
}

cmpthese( -3, {
    CONCAT  => \&concat,
    SPRINTF => \&spr_f,
    SUBSTR  => \&sub_s,
});

__END__
Your Results:
Benchmark: timing 100000 iterations of CONCAT, SPRINTF...
    CONCAT:   65359.48/s
   SPRINTF:  166666.67/s

Mine:       Rate  CONCAT SPRINTF  SUBSTR
CONCAT   98370/s      --    -62%    -66%
SPRINTF 257009/s    161%      --    -10%
SUBSTR  286165/s    191%     11%      --
[download]

Looks like the substr() is fastest.

        - tye (but my friends call me "Tye")