>>11624684OP's picture is using pairs and lists with shit like "<5,b,c>" and isn't using prime factorization at all, unless that's how they defined finite sequences. I agree that thinking about computers is a great way to have intuition for Godel numbering but you still need to formalize it in some way, whether it's prime factorizatoin theorem or some arbitrary pairing function.
>>11624674I've studied a bunch of different mathematical logic branches and the one I could never get into was proof theory, every textbook I tried was completely unreadable. If you're just trying to learn Godel, I like Enderton's treatment, that's a good book for learning mathematical logic in general