Goldbach's conjecture states that every even number greater than 2 can be expressed as the sum of 2 primes.I'm interested in this function problem:Given an even natural number n greater than 2, find a natural number p such that p and n - p are both prime.  (Inputs that are not even natural numbers may be mapped to 0.)If we assume that Goldbach's conjecture is true, this function f(n) = p is a member of TFNP.  The reason for this is that we are guaranteed by our assumption that Goldbach's conjecture is true that there exists an answer to the problem, and we can easily guess this answer (it is no greater in size than n), and then verify its accuracy in linear time.Can we do any better than TFNP here?  Could there be some algorithm in PPAD that computes this, or could there even be an FP algorithm?
Is there a PPAD algorithm for computing primes that sum to even numbers?
complexity classes;nt.number theory