Finding prime numbers, even very large ones, is neither difficult nor useful; there are simple algorithms for determining the primality of a number which don't

Finding prime numbers, even very large ones, is neither difficult nor useful; there are simple algorithms for determining the primality of a number which don't require extraordinary amounts of computing power to execute. Even factoring large semiprimes isn't inherently useful -- it's an interesting mathematical exercise, but isn't a goal unto itself.