---
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 $N(p,q) = \sum_{n=0}^q T_n \times p^n$ with $T_n$ generated by the following random number generator:

$$\begin{align}
  & S_0 = 290797 \\\\
  & S_{n + 1} = {S_n}^2\bmod 50\\,515\\,093 \\\\
  & T_n = S_n\bmod p
\end{align}$$

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 $NF(3,10000) \bmod 3^{20} = 624\\,955\\,285$.

Find $NF(61,{10}^7)\bmod {61}^{10}$.

# --hints--

`enormousFactorial()` should return `605857431263982000`.

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

# --seed--

## --seed-contents--

```js
function enormousFactorial() {

  return true;
}

enormousFactorial();
```

# --solutions--

```js
// solution required
```