Problem 133Published on Friday, 1st December 2006, 06:00 pm; Solved by 3301; Difficulty rating: 50%
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(6) = 111111.
Let us consider repunits of the form R(10n).
Although R(10), R(100), or R(1000) are not divisible by 17, R(10000) is divisible by 17. Yet there is no value of n for which R(10n) will divide by 19. In fact, it is remarkable that 11, 17, 41, and 73 are the only four primes below one-hundred that can be a factor of R(10n).
Find the sum of all the primes below one-hundred thousand that will never be a factor of R(10n).