Waring's prime number conjecture

Waring's prime number conjecture is an extension of Waring's problem, which originally deals with the representation of natural numbers as sums of a fixed number of powers of natural numbers. Specifically, Waring's problem states that for any natural number \( k \), there exists a minimum integer \( g(k) \) such that every natural number can be expressed as the sum of at most \( g(k) \) \( k \)-th powers of natural numbers.