For sufficiently large values of 'large', large primes are hard to generate. If (that's a big if) we had an efficient method to compute this number to arbitrary precision, we could compute primes of a billion or more bits.

Is there any point to generating primes that large? I thought one of the reasons to prefer ECC was because it uses a much smaller key than RSA.

A) A publication.

B) Eternal fame.

C) Money. See https://www.eff.org/awards/coop

And, most importantly, it may advance mathematics.