[taneliv]

Isn't basic research always like that? According to Wikipedia[1]: "aim of improving scientific theories for better understanding and prediction of natural or other phenomena". There is no implied success (it's only an "aim"), or utility, beyond that for science itself.

How much we want to support that (financially, socially etc) is a question a bit like, how much do we want to support children playing. Some disagree such should be supported at all, others are indifferent about such, yet others take pride in supporting or having supported such. The answer, to both of those questions, does have a large effect on how our societies look like. However, answering in the affirmative to support does not guarantee any positive progress. Likewise, answering in the negative, does not prevent progress, or basic research or children's play from happening.

[1] https://en.wikipedia.org/wiki/Basic_research

[jojobas]

Science often discovers and quantifies natural phenomena that are useful outside science. Whether pure math dealing with gazillion-digit-long primes can be of any use outside of satisfying curiosity is unclear.

[taneliv]

Aren't some modern digital cryptography methods based on exactly that?

I do agree on the view that science often discovers useful phenomena. What I tried to stress was that basic research does not, by definition, aim for such utility. Especially with pure math, whether there are any applications for new, even groundbreaking discoveries, is often very unclear. And when there are, they might be only utilized decades or centuries after the initial discovery.

[zmgsabst]

We’re really bad at handling large, complex structures.

Mathematics dealing with large primes and their complex structures is likely to find applications in other complex structures, eg in physics or computer science.

Mathematics is modern ontology: even when its self-investigation is not directly applicable, the vocabulary and semantics developed is often useful for articulating other truths.

[ndsipa_pomu]

Large primes are already useful for encryption - whether that would ever need gazillion-digit-long primes is questionable.