on the Riemann  Hypothesis was ture discovered and the eventual proof by yu-tang Hong senior engi...

even the very convincing evidence were both euler's products and grand riemann hypotheses (GRH)  are false,but the  famous millennium prize of for the Riemann Hypothesis is ture.because of every sufficiently large odd integer is the solution of non-trivial zeros which there are infinitely many,then the prime number theorem gives a formula for the number of primes less than x,in fact,n=p^kn was an irrational number, but p is an  odd primes were not easy to determine  or representation,for example,zeta (2)=pi^2/6=pi^2/24+f(p^2)/8,it was easy to determine e^(f(p^2))=t(21638)=1933.69 is ture real value.zeta(4)=pi^4/90=zeta(4)/16+f(p^4)/80,clearly f(p^4)=t(22)=81.174243,that is we gives a convincing evidence and very excellent formula some deeper information about the zeros of zeta ,with some philosophical comments,the problem has resisted the efforts of many of the finest mathematicians and that it now carries a financial reward,it is not surprising that it has attracted so much attention.by more sophisticated tools,let zea (2n)*(1-1/2^2n)=f(p^2n)/(3^(2n)-1),we have f(p^2n)=tx is an countable really number ,very positive integer x also countable .precisely t(x+1) also countable corresponding to each really number.even x is very sufficiently large.that is we have led to the new information about the zeta and can be able to look into the future.and the final solution by xiamen electronics senior engineer yu-tang Hong in 2026 year is a great in the history of mathematics.yu-tang Hong deployed his new ideas and methods with great technical mastery and described the results he obtained with elegant brevity.mathematics has been deeply enriched. zeta(3)/f(p^3)=8/189=1/t(3)=h(3);h(5)=1/t(99);h(7)=1/t(1674);.......;    f( p^6)=t(437);f(p^8)=6586.748=t(6244).that is implied that all the zeta function are countable only and if only overall non-trivial zeros behavior was observed.even pi values is a transcendental number, I am an optimist and don't contemplate such a  world. so I spend all my retirement time exploring the super difficult problems.