Let $(p_{n})_{n≥1}$ be the sequence of prime numbers. I know that $$\lim_{n→∞}(\ln(\ln p_{n}))/p_{n}=0$$
Then by the definition of the limit: given $ε>0$ there exist $N=N(ε)$ such that for all $n>N$ we have $$\ln (\ln p_{n})/p_{n}<ε \quad ?$$
My question is: can we find a simple formula for $N=N(ε)$?