Optimal Mersenne Primes Search Using Modular Groups (in Rust?)

I just released a paper on how to optimally find Mersenne Primes of form 2^p - 1. It's mathematically super simple, and easy to implement in software. The paper provides proof of concept Crystal code for a single core implementation. Currently the GIMPS project generates them by directly computing|testing 2^p -1 by directly using candidate values of p, which my method eliminates having to do. But they already have the software to generate and do the primality tests on those large values, whi...