---
id: 5900f48d1000cf542c50ff9f
challengeType: 5
title: '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
## Instructions
## Tests
```yml
tests:
- text: euler288() should return 605857431263982000.
testString: assert.strictEqual(euler288(), 605857431263982000, 'euler288() should return 605857431263982000.');
```
## Challenge Seed
```js
function euler288() {
// Good luck!
return true;
}
euler288();
```