Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. No great mathematicians study prime problems and prove Riemann hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function J₂ (ω) we prove that the new prime theorems (941)-(990) contain infinitely many prime solutions and no prime solutions.