sentences:  For example, by Lagrange's four-square theorem, the set of square numbers is an additive basis of order four, and more generally by the Fermat polygonal number theorem the polygonal numbers for formula_2-sided polygons form an additive basis of order formula_2.Similarly, the solutions to Waring's problem imply that the formula_2th powers are an additive basis, although their order is more than formula_2.By Vinogradov's theorem, the prime numbers are an asymptotic additive basis of order at most four, and Goldbach's conjecture would imply that their order is three.