Question

Let ‘P’ be a prime number such that $P \ge 11$,
let $n = P! + 1$ .
The number of primes in the list $n + 1, n + 2, n + 3,...., n + P - 1$ is

• A. P - 1
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (D)

For $1 \le i \le P-1 ; \, \, P !$ is divisible by i + 1
Then n + i = P! + (i + 1) is divisible by i + 1 for $1 \le i \le P - 1$
$\therefore $ None of $n + 1 , n + 2 ,......n + P - 1 $ is a Prime