Prove that Th(N, +, .) has uncountably many 1-types over some finite set

Question

not sure how to go about answering the above question. Thanks for your help! (alternative: Prove that Th(N, +, .) has uncountably many n-types over the empty set.)

Answer 1

Hint: try to find pairwise inconsistent partial types such that each of them corresponds to a subset of the prime numbers