freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-288-an-enormous-factorial.md

id	title	challengeType	forumTopicId	dashedName
5900f48d1000cf542c50ff9f	Problem 288: An enormous factorial	5	301939	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
```