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---
id: 5900f3f21000cf542c50ff04
title: 'Problem 133: Repunit nonfactors'
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challengeType: 5
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forumTopicId: 301761
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dashedName: problem-133-repunit-nonfactors
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---
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# --description--
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A number consisting entirely of ones is called a repunit. We shall define $R(k)$ to be a repunit of length $k$; for example, $R(6) = 111111$.
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Let us consider repunits of the form $R({10}^n)$.
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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 $R({10}^n)$ will divide by 19. Remarkably, 11, 17, 41, and 73 are the only four primes below one-hundred that can be a factor of $R({10}^n)$.
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Find the sum of all the primes below one-hundred thousand that will never be a factor of $R({10}^n)$.
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# --hints--
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`repunitNonfactors()` should return `453647705` .
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```js
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assert.strictEqual(repunitNonfactors(), 453647705);
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```
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# --seed--
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## --seed-contents--
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```js
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function repunitNonfactors() {
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return true;
}
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repunitNonfactors();
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```
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# --solutions--
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```js
// solution required
```