Re: Math is hard
"Computing the n-th Mersenne prime "
I'm not certain, but my recollection is that they are not calculating the sequence of Mersenne primes, and that if we had a method for calculating the n-th one then there is a possible inductive proof of the finite/infinite nature of them.
What we have is a method of creating potential Mersenne primes (as described in the article) using existing primes and methods to test if these are in fact prime.
"does not add a iota to the the proof that the set of Mersenne primes is finite, infinite or that this is an undecidable conjecture."
Wasn't your "proof" attempting to show that they are in fact finite? Perhaps I misunderstood.
Being able to compute continually larger Mersenne primes may not prove that they are infinite, but may be close enough for practical purposes. In the same way you can't prove linear optimizations are efficient, but in application they are, the set of Mersenne primes may be large enough to be close enough to infinity for the purpose at hand.