Question

Let P be a prime number such that P  23. Let n = p! + 1. The number of primes in the list n + 1, n + 2, n + 3, … n + p – 1 is

Solution

Correct option is

0

For 1 ≤ k ≤ p – 1, n + k = p! + k + 1, is clearly divisible by k + 1. Therefore, there is no prime number in the given list. 

SIMILAR QUESTIONS

Q1

The exponent of 7 in 100C50 is

Q2

In the certain test there are n questions. In this test 2k students gave wrong answers to at least (n – k) questions, where k = 0, 1, 2, …, n. If the total number of wrong answer is 4095, then value of n is 

Q3

If n > 1 and n divides (n – 1)! + 1, then 

Q4

In a group of 8 girls, two girls are sisters. The number of ways in which the girls can sit so that two sisters are not sitting together is

Q5

The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with T is

Q7

The number of subsets of the set A = {a1a2, … an} which contain even number of elements is

Q8

The number of ways in which we can post 5 letters in 10 letter boxes is

Q9

The number of five digit telephone numbers having at least one of their digits repeated is

Q10

The term digit of 1! + 2! + 3! + … + 49! Is