# How Many 8's?

Let $$x_n$$ be defined as the smallest positive integer satisfying $\large x_n ^3 \equiv \underbrace{888\ldots 8}_{n \text{ 8's}} \pmod{10^n} .$

Find $$\displaystyle \dfrac12 {\sum_{n=1}^{8} x_n}$$.

Hint: $$x_1=2$$ and $$x_2=42$$. The answer is a prime number as well.

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