The large primes themselves don't have much use as far as I am aware, but the methods and tools developed to find them have apparently been quite helpful in oth

The large primes themselves don't have much use as far as I am aware, but the methods and tools developed to find them have apparently been quite helpful in other fields. This is much the same argument for why the LHC is a good idea. The people who care about Higgs bosons proper are quite few.