A Characteristic Function for the Primes

I develop a function that, for any integer $n \geq 2$, takes a value of 1 if $n$ is prime, 0 if $n$ is composite. I also discuss two applications: First, the characteristic function provides a new expression for the prime counting function. Second, the components of the characteristic function point to a new expression that gives the number of distinct prime factors for any integer greater than one.