about regexpes,as ikegami offered,
my humble imput, turn every number into a letter from a to t
0 - 19 and match the original line upon every:

$v[$i++] = $_ for 'a'..'t';

@a = qw/2 13 3 16/;
$a = join '', map {$v[$_]} @a;

#generating 1 000 000 base of numbers

for (0..1000000){
    %rnd = ();
    while(keys %rnd < 4){$rnd{$v[int(rand(20))]} = undef;}
    push @b, join '', keys %rnd;
}

#doing search

for (@b){
    $counter++ if !/[$a]/;
}

print "$counter\n";
[download]

on my pc
1 000 000 base generated in 4 seconds,
search upon it done in 1 second
around ~370 000 unique numbers.