Proof the Riemann-Hypothesis and Goldbach’s conjecture

The Goldbach conjecture

the Riemann Hypothesis

he Riemann Hypothesis: This is one of the most famous unsolved problems in mathematics, which concerns the distribution of prime numbers. It proposes that the non-trivial zeros of the Riemann zeta function all lie on a specific line in the complex plane.

Understanding the distribution of primes can help us answer these questions and potentially lead to new insights about prime number

Let $\phi$ denote Euler's totient function, and $p, q > 1$ be primes. Conjecture and prove a formula for $\phi(pq)$ in terms of $p$ and $q$.