I just released this paper (extracted from a larger journal article slated for Dec 2026) which uses Crystal code to show how to sequentially generate Mersenne Primes without computing 2^p - 1.
The code is the single core version. I haven’t had a chance yet to do the multi-core parallel version.
As these numbers become humongously large, it would require special software to generate and check 100s of digits values.
It would be nice if there could be some Crystal hooks into such existing software, to be able to write and run complete MPGS searches with it. So if anyone knows how to do that, or feels inspired to try, let me know.
https://www.academia.edu/178745494/Optimal_Mersenne_Primes_Search_Using_Modular_Groups