data/problems/133.yml
---
:id: 133
:name: Repunit nonfactors
:url: https://projecteuler.net/problem=133
:content: |+
A number consisting entirely of ones is called a repunit. We shall define R(<var>k</var>) to be a repunit of length <var>k</var>; for example, R(6) = 111111.
Let us consider repunits of the form R(10<sup><var>n</var></sup>).
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 <var>n</var> for which R(10<sup><var>n</var></sup>) 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(10<sup><var>n</var></sup>).
Find the sum of all the primes below one-hundred thousand that will never be a factor of R(10<sup><var>n</var></sup>).