Numbers bigger than memory

[Pi]

Hello

I was trying to compute hyperpowers, such as 8^7^6^5^4^3^2, or 7^^7, in
order to further perform  operations such as modular arithmetic. And I've
found that all programs I know cast an overflow error.

It would be nice that GMP could be able to use numbers larger than memory.
Maybe using ...
...some fast in-memory compression algorithms.
or
... being able to work directly with disk databases.
or even
... allowing distributed computation.

Regards