---
id: 5900f3db1000cf542c50feee
challengeType: 5
title: 'Problem 111: Primes with runs'
---

## Description
<section id='description'>
Considering 4-digit primes containing repeated digits it is clear that they cannot all be the same: 1111 is divisible by 11, 2222 is divisible by 22, and so on. But there are nine 4-digit primes containing three ones:
1117, 1151, 1171, 1181, 1511, 1811, 2111, 4111, 8111
We shall say that M(n, d) represents the maximum number of repeated digits for an n-digit prime where d is the repeated digit, N(n, d) represents the number of such primes, and S(n, d) represents the sum of these primes.
So M(4, 1) = 3 is the maximum number of repeated digits for a 4-digit prime where one is the repeated digit, there are N(4, 1) = 9 such primes, and the sum of these primes is S(4, 1) = 22275. It turns out that for d = 0, it is only possible to have M(4, 0) = 2 repeated digits, but there are N(4, 0) = 13 such cases.
In the same way we obtain the following results for 4-digit primes.

Digit, d
M(4, d)
N(4, d)
S(4, d)
0
2
13
67061
1
3
9
22275
2
3
1
2221
3
3
12
46214
4
3
2
8888
5
3
1
5557
6
3
1
6661
7
3
9
57863
8
3
1
8887
9
3
7
48073

For d = 0 to 9, the sum of all S(4, d) is 273700.
Find the sum of all S(10, d).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler111()</code> should return 612407567715.
    testString: assert.strictEqual(euler111(), 612407567715, '<code>euler111()</code> should return 612407567715.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler111() {
  // Good luck!
  return true;
}

euler111();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
