Irrationality measure and lower bounds for pi(x)

In this note we show how the irrationality measure of $zeta(s) = pi^2/6$ can be used to obtain explicit lower bounds for $pi(x)$. We analyze the key ingredients of the proof of the finiteness of the irrationality measure, and show how to obtain good lower bounds for $pi(x)$ from these arguments as well. Whi