Sum of Reciprocals of Primes is Divergent

Theorem

 * $\displaystyle \sum_{p \in \Bbb P}^n \frac 1 p > \ln \left({\ln \left({n}\right)}\right) - \ln \left({\frac{\pi^2}2}\right)$


 * $\displaystyle \lim_{n \to \infty} \left({\ln \left({\ln \left({n}\right)}\right) - \ln \left({\frac{\pi^2}2}\right)}\right) = + \infty$