HMMT 2023 U34

The number 2027 is prime. For $i=1,2, \ldots, 2026$, let $p_{i}$ be the smallest prime number such that $p_{i} \equiv i(\bmod 2027)$. Estimate $\max \left(p_{1}, \ldots, p_{2026}\right)$. Submit a positive integer $E$. If the correct answer is $A$, you will receive $\left\lfloor 25 \min \left((E / A)^{8},(A / E)^{8}\right)\right\rfloor$ points. (If you do not submit a positive integer, you will receive zero points for this question.)