I was wondering about what you said: whether the speed-up does rely on providing an outright string into the regex

my $n = 112358;
...
[download]

I guess, it does rely on it. Not much but look at it from the processor's perspective. It is an assignment operation hence there will be an extra "mov" instruction moving data from the accumulator to say the DX register, right? Whereas providing an outright string will take data directly from the accumulator.

Note

My explanation is open for abuse... :D