## Large repunit factors

### Problem 132

Published on Friday, 1st December 2006, 06:00 pm; Solved by 4161; Difficulty rating: 45%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 = 11×41×271×9091, and the sum of these prime factors is 9414.

Find the sum of the first forty prime factors of R(10^{9}).