If $$n= 2006!+1$$ Then number of primes among $$n+1,n+2\ldots n+2005$$ are
I concluded that $2006!$ can never be prime and will end with $0$. That is $n$ is odd number ending with $1$,hence $n+1,n+3,n+5\ldots n+2005$ cannot be prime.It leaves almost half the numbers. Now how should i proceed?
Suppose $1<k\leq2006$. Then $k$ is a factor of $2016!$, and also of $2016!+k$, which equals $n+(k-1)$. Thus, each number in your list has a factor greater than $1$, and is therefore not prime.