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Let $f(x)$ be a non-linear polynomial over $\mathbb{Z}$.
Consider the following sum $\pi_f(x):= \#\{y: y< x \text{ and } f(y) \text{ is prime} \}$.
Can we get an upper bound for $\# \pi_f(x)$$\pi_f(x)$?
Can we get an upper bound for $\# \pi_f(x)$?
Can we get an upper bound for $\pi_f(x)$?
