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

# --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

# --hints--

`euler288()` should return 605857431263982000.

```js
assert.strictEqual(euler288(), 605857431263982000);
```

# --seed--

## --seed-contents--

```js
function euler288() {

  return true;
}

euler288();
```

# --solutions--

```js
// solution required
```
