Endpoint estimates for the maximal function over prime numbers

Given an ergodic dynamical system $(X,\mathcal{B},\mu ,T)$, we prove that for each function $f$ belonging to the Orlicz space $L(\log L)^2(\log \log L)(X, \mu)$, the ergodic averages $$\frac{1}{\pi (N)}\sum _{p\in {\mathbb{P}}_N}f\left(T^{p}x\right),$$ converge for $\mu$-almost all $x\in X$, where ${\mathbb{P}}_N$ is the set of prime numbers not larger that $N$ and $\pi(N) = # $\mathbb{P}$_N$.