[eigenket]

By the way, if you're wondering if anyone has done anything useful with the method of describing numbers as prime exponents I mentioned the answer is yes, depending on your definition of "useful".

The encoding in terms of prime exponents is known as the Godel encoding, and its a fairly important step in proving things like Godel's incompleteness theorems and the undecidability of the Halting problem.

Essentially it's a one-to-one map between natural numbers and finite sequences of natural numbers (since you can encode (a,b,c,d...) as 2^a × 3^b × 5^c × 7^d etc), which turns out to be mathematically a convenient thing to have.