The Riemann zeta function is one of the most Euler's important and fascinating functions in mathematics. By analyzing the material of Riemann's conjecture, we divide our analysis in the ζ(z) function and in the proof of the conjecture, which has very important consequences on the distribution of prime numbers. The proof of the Hypothesis of Riemann result from the simple logic, that when two properties are associated, (the resulting equations that based in two Functional equations of Riemann), if we zero these equations, ie ζ(z) = ζ (1-z)= 0 and simultaneously they to have the proved property 1-1 of the Riemann function ζ(z), the hypothesis will be true.Thus, there is not margin for to non apply that the Re (z)=1/2 {because simple apply ζ (z) = ζ (1-z)=0 and also ζ(z) as and ζ(1-z) are 1-1}.This, after it stands, will gives the direction of all the non-trivial roots to be all in on the critical line, with a value in the real axis equal 1/2. Part I. Proof Riemann Hypothesis from Theorems 1,2,3. The R-Hypothesis focuses on the point where we must prove that if s = Re(s) + Im(s)*I .. i) The functions ζ(s) and ζ(1-s) are 1-1 on the critical strip. ii) The common roots of the equations ζ(s)-ζ(1-s) = 0 they have Re(s)=Re(1-s)=1/2 within the interval (0,1) and determine unique position, which is called critical line. In Part II, we examine the distribution of prime numbers. The complexity of the Riemann Hypothesis is not limited to any method of proving that Re(z)=1/2 for the function ζ( ). It is a multidimensional issue that has many dimensions in physics as well as in other sciences. Anyone who says he has completely solved the hypothesis will be incomplete as to the possibilities it contains and the methods he can use to get some insight that comes close to some truths concerning it. With this in mind if we ask to prove that the hypothesis is correct, we must ask for the values of the critical lines that confirm the Riemann hypothesis. However, the Riemann hypothesis does not hold only in the interval (0,1) in the generalized form of the Zeta-functions ,but in the generalized form several critical lines arise within the intervals (-1,0) or (1,+∞) or (-∞,-1) specifically example, in the cases of the general equation ζ(q*z)=0,q>1/2 or q<-1/2 or (01/2 in R, G-z(z,q)=0 for 3 general cases out of 5, and for case Davenport Heilbronn case, which has zeros of a Dirichlet series periodic.Therefore, whether or not the Riemann Hypothesis holds depends on whether or not we accept the fact if we consider only ζ(z)=0. If in the definition of the Hypothesis the other forms or part of them also hold , i.e. ζ(q*z)=0 or ζ(q,z)=0 or ζ(z,q)=0 with q∊R in general or the Epstein Function or the Dirichlet series and others, then the Hypothesis does not hold in general, but only in special cases which are stated in detail.But we have to accept an indisputable fact that in order to have a visual perception of which ζ-functions have zeros with Re(z)=1/2 or have Re(z) different from 1/2 or other critical lines outside the interval (0,1), we have to solve transcendental equations with accuracy. This can only be achieved with the generalized theorem , and with the Periodic Radicals or Lagrange Method (https://arxiv.org/search/ query=mantzakouras +&searchtype =all&source=header) , work that has already been published. This makes it a unique reality and in this respect it has to be clarified , which ζ-functions we accept when we talk about proving the Riemann Hypothesis. "The question, dear colleagues, is not simply whether or not Riemann's Hypothesis is valid, but what ζ- functions do we accept that the Hypothesis as defined by Riemann includes? Or must we admit the general view of existing ζ-functions that Hypothesis includes. So if we take as a general assumption of the Hypothesis all the parallel ζ-functions then it is not 100% true. Of course it is also true that the Riemann hypothesis has multiple interconnections with other sciences and gives directions appropriate and grouped, depending on the function that we will accept to be valid in each specific case of application.The R-H applies only when we have specific cases mentioned in this document and perhaps and in others, but not in general, If we accept the generalized ζ- functions .This is considered as the only real answer to the conjecture of the Riemann Hypothesis that has stunned the mathematical community for more 200 years", Cases I,II of the characteristic generalized equation G-ζ(z,q)=0, {q=(a+b)/a, q>0} ,|q|<1 or |q|>1,q∊R as well as the cases of ζ(q*z)=0 with q>1/2 are subclass of the generalized one mentioned above, and some cases of the Dirihlet series reject the Riemann Hypothesis. So if the hypothesis is formulated as follows: "For any z-function, the zeros of the resulting equation coincide on the critical line with Re(z)=1/2, the formulation is complicated as a Latent and the Hypothesis does NOT hold". But if it is formulated as "The zeros only of ζ(z)=0 coincide on the critical line for Re(z)=1/2 is correct and the Hypothesis is Valid", as has been shown. Obviously this happened because the equations of other related functions i.e. other related equations arising from related functions with the function z were not completely or adequately solved or not at all and there was a large knowledge gap related to where their zeros are located with respect mainly to the interval (0,1).These equations are forms of Transcendental equations quite difficult and to solve them a strong method and a generalized Theorem for solving such equations is needed.