Technology

Have you ever heard of the Riemann hypothesis? Since 1859 it's yet to be solved. The generalization of prime numbers (i.e. a function f(n) that yields the nth prime) would impact fields such as Navigation Systems and Traffic Management, Communication Systems and Satellite Communication (i.e. your Internet connection could become more efficient and faster), Astrophysics and Cosmology, Quantum Mechanics, AI and Machine Learning, E-commerce, Finances and Algorithmic Trading, among many other fields. (Yeah, it seems like nothing. /s)

Does it need to? Does anything need to? I'd argue that humans toying with the novelty of 'seemingly useless' things has enriched humanity by a whole lot. Archmedes basically dicking around doing fuck all in that shed of his instead of growing crops

If we can analyze larger primes, we can generate larger primes which has applications in math, particularly cryptography and other areas, not even beginning to look at number theory. Specifically being able to verify them over a cloud is useful, we can generate them quicker and worry about their safety less. https://en.wikipedia.org/wiki/Hensel's_lemma has uses in physics actually.

Oh, you mean you don't understand it, gotcha.

Yes, and Bayesian statistics are useless too, they're all about things that have already happened!