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Interesting news. I missed it. Some years ago I've contributed to checking that Mersenne Prime candidates are true primes. And I learnt a lot about how it is done. At least about the theoretical stuff, not about how the computation is done with a FFT. And this "theoretical" stuff deals with the proof that enables to say if a Mersenne number is prime or not, which is called: LLT : LucasLehmer Test, based on the name of the two guys who provided fundamental work. Lucas built the idea and he provided notperfect proofs. And then later Lehmer provided complete and clear proof. How this LLT proof works is astonishing. Proving it may be very complex, but understanding how it works is easy and funny. I think that you should talk about this LLT mechanism here. I could help if needed. Contact me at: tony(.)reix[@]laposte(.)net . Regards. Grenoble. France