HMMT November 2024 U34

The largest known prime number as of October 2024 is $2^{136279841}-1$. It happens to be an example of a prime number of the form $2 x^{2}-1$. Estimate the number of positive integers $x \leq 10^{6}$ such that $2 x^{2}-1$ is prime. Submit a positive integer $E$. If the correct answer is $A$, you will receive $\left\lfloor 20.99 \max \left(0,1-\frac{|E-A|}{A}\right)^{2.5}\right\rfloor$ points.