Neat! Don't miss the (heuristic) argument in the comment by Tim Gowers about why 82000 was lucky, and that there may not be any other larger number with the same properties.
The argument isn't saying that arithmetic is random. It's saying that a lot of properties of number systems behave as if they are random.
A good example is finding arithmetic sequences of length K in the prime numbers (for example, the sequence 3, 5, 7 is an arithmetic sequence of length 3, as is 17, 23, 29). It can be shown that random sets that have a density similar to the primes (i.e. the chance that N is in the set is proportional to 1 / log(N)) have arbitrarily long arithmetic sequences - as, in fact, do the prime numbers.
This looks like an interesting perspective. Do you have any pointers to discussions of topics that become more intuitive/clearer when thought about in other bases ?
