Why not? Whether you're running python code in your C interpreter or just running C code, the same memory restrictions will apply based on your hardware. CPython doesn't place a lower bound on bignums over a non-C based implementation
EDIT: See the GMP library, which states "There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on"[0]
The C specification limits programs to addressing a finite amount of memory, though it can be made arbitrarily large by an implementation. The Python specifications do not imply this though real interpreters do.
> though it can be made arbitrarily large by an implementation
Yes, this is my entire point
Why should I care what the language specification states in a computability theory discussion? There only needs to exist a method to accomplish our goal-Whether the method conforms to specification or not doesn't seem relevant to me.
Would it be fair to say then that "Python" is Turing complete, while CPython/PyPy implementations are not turing complete, because they will always implicitly run up against C's memory limitations, therefore they do have a hard limit. Python itself as a language is turing complete because it does not place realistic limitations on the user like C does?
EDIT: See the GMP library, which states "There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on"[0]
https://gmplib.org/#WHAT