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Problem 934

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Unlucky Primes

We define the unlucky prime of a number $n$, denoted $u(n)$, as the smallest prime number $p$ such that the remainder of $n$ divided by $p$ (i.e. $n \bmod p$) is not a multiple of seven.

For example, $u(14) = 3$, $u(147) = 2$ and $u(1470) = 13$.

Let $U(N)$ be the sum $\sum_{n = 1}^N u(n)$.

You are given $U(1470) = 4293$.

Find $U(10^{17})$.

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不幸素数

定义数$n$对应的不幸素数$u(n)$为最小的、使得$n$除以$p$的余数（即$n \bmod p$）不是$7$的倍数的素数$p$。

例如，$u(14) = 3$，$u(147) = 2$，$u(1470) = 13$。

记$U(N)$为求和$\sum_{n = 1}^N u(n)$。

已知$U(1470) = 4293$。

求$U(10^{17})$。

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