Prime numbers and the Riemann hypothesis

By considering the prime zeta function, the author intended to demonstrate in that the Riemann zeta function zeta(s) does not vanish for Re(s)>1/2, which would have proven the Riemann hypothesis. However, he later realised that the proof of Theorem 3 is fundamentally flawed. The main tools of our argument are: bounds and oscillation theorems for the prime counting function, classical properties of Dirichlet series and the identity theorem for real-analytic functions.