----- the inexplicable decision to throw away all information about the exponents except whether they are zero or nonzero. ----- I just want to comment on this description, not on the visualization per se. First of all, there is no question that the quantity of information discarded is vast. But there is still a vast amount of information retained. Many wonderful mathematical discoveries have been made by forgetting a lot of information. A detailed metric space could be forgotten into a mere topological space, which could be forgotten into its homotopy groups, say (these are typically finitely generated groups {π_n}, one group for each positive integer with all but the first one abelian). And in this case, we can see identifying all positive powers of a prime factor with each other as representing — if not all integers — instead, all possible *divisibilities*: Each integer N is divisible by certain primes and not by others. Each given pattern of divisibilities is represented once and only once in this reduced information. Okay, so that's what it's actually a picture of. —Dan