---
id: 5900f48d1000cf542c50ff9f
challengeType: 5
title: 'Problem 288: An enormous factorial'
forumTopicId: 301939
---

## Description
<section id='description'>
For any prime p the number N(p,q) is defined by
N(p,q) = ∑n=0 to q Tn*pn with Tn generated by the following random number generator:

S0 = 290797
Sn+1 = Sn2 mod 50515093
Tn = Sn mod p


Let Nfac(p,q) be the factorial of N(p,q).
Let NF(p,q) be the number of factors p in Nfac(p,q).


You are given that NF(3,10000) mod 320=624955285.


Find NF(61,107) mod 6110
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler288()</code> should return 605857431263982000.
    testString: assert.strictEqual(euler288(), 605857431263982000);

```

</section>

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

<div id='js-seed'>

```js
function euler288() {
  // Good luck!
  return true;
}

euler288();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>