Question

If A(x) denotes the number of prime number not greater than x, then what is the value of A(A(100))​

Answer 1

Answer:

9

Step-by-step explanation:

Given: A(x) = number of prime numbers less than x

The number of prime numbers less than 100 can be written as:

Prime numbers less than 20 = 2, 3, 5, 7, 11, 13, 17, 19

Prime numbers between 20 and 40 = 23, 29, 31, 37

Prime numbers between 40 and 60 = 41, 43, 47, 53, 59

Prime numbers between 60 and 80 = 61, 67, 71, 73, 79

Prime numbers between 80 and 100 = 83, 89, 97

A(100) = Number of prime numbers less than 100 = 25

Now, A(A(100)) = A(25) = Number of prime numbers less than 25 = 9