Can you play the game of Sophie and Emmy?

From the first question, we know that $n$ is of the form $11k+3$ , meaning it is one of: $(3,14,25,36,47,58,69,80,91)$

Writing this list in terms of its prime factors: $(3,2 \cdot 7,5 \cdot 5,2 \cdot 2 \cdot 3 \cdot 3,47,2 \cdot 29,3 \cdot 23,2 \cdot 2 \cdot 2 \cdot 2 \cdot 5,7 \cdot 13)$

Now, our answer is the number of primes that only appear once in the above list: $(13,23,29,47)$ , so the answer is $\boxed{4}$