Find out the number of prime numbers

Interesting extension: There are $22$ known $n$ for which $n!+1$ is prime ( $2019$ is not one of them). It is conjectured (but still an open question) that there are infinite such $n$ .

See Factorial Primes

If we take a general case: $n + k$ , where $k = 2,3,4 ... 2019$

$n = 2019! = 2019(2018).....(k)....(2)(1)$

$\therefore$ we can express $n + k$ as $k(\frac{2019!}{k} + 1)$ , where $k = 2,3,..2019$ which is divisible by $k$ . So no prime numbers exist between $n + 2$ and $n + 2019$ .