Eccoci.

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