Number of primes in $[30! + 2, 30! + 30]$ How to find number of primes numbers $\pi(x)$ in $[30! + 2$ , $30! + 30]$, 
where $n!$ is defined as:
$$n!= n(n-1)(n-2)\cdots3\times2\times1$$
Using Fermat's Theorem:
$130=1\mod31$,
(since $31 \in \mathbb{P}$). This implies the above is congruent to $17\mod31$.
This is correct, right?

Observe that 
$$n!+m$$ is divisible by $m$ for $2\le m\le n$ and integer $n\ge2$
So, we can have an arbitrarily large sequence of composite numbers for an arbitrary large value of integer $n$ 
