Collisions

Remember the factorial $n! = 1*2*3*...*n$. We want to store a hash table of all the factorials up to $100!$ and we want to use a hash function of the form $h(n) = n\ \%\ p$. Which would be a good value for $p$?

You can consider that the hash table has more than $p$ buckets and that we can fit numbers up to $100!$ in variables.

Tips for those who don't love math:

1. The reminder of $n!$ with $n, \; n-1, \dots , 2$ is equal to $0$. Why?

2. $105 = 3 * 5 * 7$

3. $101$, $47$, and $5$ are prime numbers.