For each rational prime p let **X**<sub>p</sub> denote the random variable uniformly distributed in {0, 1, ..., p-1} with all the **X**<sub>p</sub> independent of each other. Define the coset **C**<sub>p</sub> of the prime ideal pℤ via 

**C**<sub>p</sub> = pℤ + **X**<sub>p</sub>.

Let **S** be the random variable equal to the size of the complement of the union of all the **C**<sub>p</sub>:  

   **S** = card(ℤ - (**C**<sub>2</sub> ∪ **C**<sub>3</sub> ∪ **C**<sub>5</sub> ∪ ...)).

What is the expected value of **S** ?

(In the simplest case with all **X**<sub>p</sub> = 0, we get **S** = 2.)