Yup. Math behind CT scan was developed in 1917. It was 50-ish years later it would be put to practical use. https://en.wikipedia.org/wiki/Radon_transform

Apples and oranges. Naming more mersenne primes does not constitute discovering new mathematics. It's really very hard to argue that this is a good use of computing power.

I think people will continue to search and observe things that they are unable to predict. This is true in almost any field.

Sure, pure mathematical theory has a tendency to become useful later, but finding specific Mersenne primes is not pure math.

It’s not known if there is an infinite number of Mersenne primes (though it is strongly suspected) - so an interesting mathematical object to discover would be ‘the largest Mersenne prime’ - but this process isn’t going to find that (it might find a candidate but it won’t find a proof). If there are indeed infinite Mersennes then this search is just guaranteed to keep finding more forever.

It’s like looking for green pebbles on a beach. It’s nice when you find one to add to your collection, but it’s not that surprising, and if you keep looking you’ll probably find more. You’re not advancing geological knowledge if you keep looking and finding more.

Yes but if you want to say if there are an infinite number of green pebbles on an infinitely large beach then the problem you need to solve is finding the distribution of the green pebbles on the beach. It's only possible to do that once you've found a few green pebbles and gets much easier if you've found many.

We don't know whether the search for further Mersenne primes eventually gives birth to a new algorithm which will enable further advances in other fields.

Cranking on the current best known algorithm for testing for Mersenne primes does nothing to advance the state of the art for other algorithms, though.

It’s like saying, we have a project that keeps sorting larger and larger sets using quicksort because we believe it will help advance the state of sorting algorithms. ‘We just sorted the largest ever set!’

It can provide fuel for said algorithm.

I'm all for putting work to find things out and I agree with you, but for the sake of argument:

Say these are really relevant 200 years down the line, maybe even 100 or 50, does it really make sense to calculate them now, given that computers 50, 100 and 200 years from now will outperform ours by orders of magnitude?

Looking at this as reference: https://en.wikipedia.org/wiki/Microprocessor_chronology

Say you grab a CPU from the end of the 70s and get it working until now, that'd be about 13*10e15 operations, or about a month of processing in a modern 5GHz CPU. That's 40 years to a month.

Mathematics tends to be upstream of technology. I would expect that improvements in mathematical knowledge in general will help us construct even better computers in the future. We are slowly approaching some physical limits, but algorithmic improvements may get us further speed improvements.

IDK about this particular scientific team, but if you have to run a long-running task, you will be a lot more careful about complexity and speed of your data and algorithms instead of relying on brute force. Maybe you will actually discover some real improvements of existing knowledge.

I can even see the effect throughout my IT life outside science. People who cut their teeth on processors with limited power and not enough RAM tend to produce much more efficient solutions even when programming modern computers. They just don't take the gigabytes and gigahertz for granted.

Agreed with all of this, well put. I’d like to add though that we don’t do math just because we anticipate there will be some practical utility in a different field down the line. Mathematics isn’t merely a prerequisite for engineering. Does it not suffice that we study math for the sake of it?

The Mersenne primes for example are a delightful little mathematical object. IMO they are immediately curious and interesting. I am very grateful that we continue to make progress in understanding them.