Thirteen Digit ISBN

The days of the 10 digit ISBN are winding down! Starting 1/1/2007, is ISBN-13. Luckily the new ISBN system has been made backwards compatible with the old one. It seems there was always a 3-digit EAN code prefix which was always 978. Now, they're just introducing another series 979. Since the last digit in the ISBN is just a check digit, that really only gives 1 billion extra ISBN numbers. Which makes me wonder, how long can the 13 digit ISBN last before it is exhausted as well? 2100? 3000? Will we still be relying on books at that time or will all our data have become digitized and books obsolete? Or will there be some new medium by then? Just some interesting questions to ponder.

On a side note, the method of computing the check digit of the ISBN is quite interesting as well. For the 10-digit ISBN, the check digit has to be chosen such that the dot product of the vector [1..10] with the 10-digit vector representation of the ISBN (including the check digit as the first entry) should be congruent to zero modulo 11! If the check digit has to be 10, the letter X is used as the digit. Now obviously the check digit is not foolproof, but since 11 is prime, it does a pretty good job. So I wonder if for ISBN-13, the check digit will be computed modulo 13+1=14 or 13, also prime. I'm inclined to suspect that it would use modulo 13.

Anyway, this leads me to my idea for an ISBN game. So one person picks a favorite book and then finds its ISBN. He gives the other person the ISBN without the check digit and he has to go and figure out what the book is. Right now the game is fairly trivial, but you can probably add some extra steps along the way to add to the challenge. Maybe the book title can be part of a clue for a larger puzzle and maybe one other digit (besides the check digit) could be hidden as well. That at least expands the number of possible matching ISBNs - there could be other hints given to narrow down the choice. I'll have to try this sometime :)

-- Arkajit