A chain of triplets

Calculus Level 1

$S=\dfrac { 1 }{ 1\cdot 2\cdot 3 } +\dfrac { 1 }{ 3\cdot 4\cdot 5 } +\dfrac { 1 }{ 5\cdot 6\cdot 7 } +\dfrac { 1 }{ 7\cdot 8\cdot 9 } +\frac { 1 }{ 9\cdot 10\cdot 11 } +\cdots$

The sum $S$ can be expressed in the form $\ln { A } -\frac { 1 }{ A },$ where $A$ is a prime number.

What is $A?$