[vikingerik]

Nitpick, 50 is 2^1 × 5^2, not the other way around. But anyway, thanks a ton for this post, I felt my brain shift at a new way of thinking about numbers, seriously. I have to wonder what serious and useful implementations of this method might have been done somewhere.

[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.

[eigenket]

Thanks :) I edited my comment so the arithmetic is (hopefully) right now