ITMC 2018 Grade 8 National Preliminary set01 Question 23

For a nonnegative integer $n$, $n!$ is the product of all positive integers up to $n$, and $0!=1$. For example $1!=1,2!=2,3!=6,4!=24$. How many primes are in the 18-number sequence $20!+2,20!+3,\ldots,20!+19$?