Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J₂(ω) we prove that the new prime theorems (491)-(540) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. π_k(N₀,2) ≥ 1. This is the Book theorem.