problem 18i

Let $R(p)$ be the remainder when the product $\prod{x=0}^{p-1}(x^3-3x+4)$ is divided by $p$ . For example, $R(11)=0$ and $R(29)=13$ .
设 $R(p)=\prod{x=0}^{p-1}(x^3-3x+4)\mod p$ ,比如 $R(11)=0,R(29)=13$ .

Find the sum of $R(p)$ over all primes $p$ between $10^{9}$ and $1.1\times10^9$ .
求

$\sum_{i=10^9}^{1.1\times10^9}R(i),i\in prime$

题解(spoiler)

Wrong Answers

I don’t know(noob).
不会(菜).