ITMC 2018 Grade 9 National Preliminary set01 Question 23

For a nonnegative integer $n$, $n!$ is the product of all positive integers at most $n$, with $0!=1$. Examples: $1!=1,2!=2,3!=6,4!=24$. How many primes are among the 28 numbers $30!+2,30!+3,\ldots,30!+29$?