This is an objective problem 151 from TOMATO based on Consecutive composites, useful for Indian Statistical Institute Entrance Exam.
Let n = 51! + 1. Then the number of primes among n+1, n+2, … , n+50 is
(D) more than 2;
51! is divisible by 2, 3,… 51.
Hence 51! +2 is divisible by 2, … , 51! + k is divisible by k if
Therefore all of these numbers are composite (none of them are primes).
Answer is (A)
Note: The above problem can be further extended to say that for any natural number of n, we can have n consecutive composite numbers.