https://chat.openai.com/share/aadf6a17-f40e-4ea6-8f5e-236bc2...
ChatGPT 4 gives a more correct answer:
> Pi is an irrational number, meaning it has an infinite number of digits that don't repeat in a predictable pattern. So, there's no such thing as the "last" digits of pi.
https://chat.openai.com/share/6a7c0221-0aca-48af-8938-e4d98e...
> The decimal representation of pi is infinite and non-repeating, so it doesn't have "last 8 digits" in the way a finite number would. However, if you're looking for the first few digits of pi, they are 3.14159265. If you need more digits, you can find them using various sources or tools that provide the decimal expansion of pi.
A cryptographically secure pseudorandom number generator lets me pump out a stream of digits that's certainly computable, but unless you know my private key, you won't be able to predict it.
(Finding out the private key from the stream is 'computable', because the definition of computable is comfortable with running exponentially long brute force searches. But that's why 'computable' is not a useful definition in practice. You want something that captures 'tractable', not just 'possible on a Turing machine at all'.)
The most intuitive answer is just computability.
If you have finite memory, you have a finite number of states and will eventually return to a previous state. In your example, you eventually will run out of memory to track the number of consecutive zeros.