Question

Let p be a prime ≥ 3. Let n = $\angle p$ + 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)

0

Answer 2

For 1 ≤ k ≤ p – 1,

n + k = ($\angle p + 1)$ + k = $\angle p$ + (k+1) is clearly divisible by k+1 as 2≤k+1≤p and hence $\angle p$ does contain the factor k+1.

($\because$1≤ k ≤ p – 1, $\therefore$ 2≤k+1≤p)

So, there is no prime in the given list.