Nice. You have a typo here: f(21) = (23 * 854) % 1000 = 17934 % 1000 = 934. I wouldn't be surprised if the last four digits are some form of built-in barcode

Nice. You have a typo here: f(21) = (23 * 854) % 1000 = 17934 % 1000 = 934. I wouldn't be surprised if the last four digits are some form of built-in barcode error checking, and are not used anywhere else.