HMMT 2025 U35

Call an 8-digit number a flamingo if it uses each of the digits 2 through 9 exactly once. Estimate the number of flamingos that are prime.

Submit a positive integer $E$ . If the correct answer is $A$ , you will receive round $\left(20 \cdot \min \left(\frac{A}{E}, \frac{E}{A}\right)^{21}\right)$ points.