one small integer is not enough, two small integers are better (lab journal initials/number and sample number, like AC7-295. something like AC7-295A, then AC7-295B and so on if needed. that's how i do it anyway) this way there's no possibility of mixup with other people's samples and samples described in old lab journals
But if they do get jumbled, sorting them back out into different experiments, batches or subjects or time periods might make you prefer some extra info accesible by eye.
If you've got a robot sorter maybe a qr code - but you'd have to be pretty large scale for that to be cheaper than a human.
As someone who lived through Y2K not using 4 digits for year just makes me itchy. The rest would be fantastic for a large multi building setup like Mayo.
It's cause they're lazy and don't stop the pen when they get to the part where they're supposed to double back. They draw a circle so they can keep the pen moving and save energy.