Prime Trouble

For any positive integer $n > 1$ , let $P(n)$ denote the largest prime not exceeding $n$ . Let $N(n)$ denote the next prime larger than $P(n)$ ,

Then Evaluate: $\large \frac{1}{P(2)N(2)}+\frac{1}{P(3)N(3)}+\frac{1}{P(4)N(4)}+\cdots+\frac{1}{P(2016)N(2016)}$

Clarification: $P(10) = 7$ and $N(10) = 11$ , while $P(11) = 11$ and $N(11) = 13$ .

Note: If your answer is of the form $\dfrac{a}{b}$ , where $a,b$ are coprime positive integers, then submit $a+b$ .