A number consisting entirely of ones is called a repunit. We shall define $R(k)$ to be a repunit of length $k$.
For example, $R(10) = 1111111111 = 11 \times 41 \times 271 \times 9091$, and the sum of these prime factors is $9414$.
Find the sum of the first forty prime factors of $R(10^9)$.
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