Math Number Theory
Intermediate Level

Implement the countPrimeNumbersUpToN method that counts all prime numbers from 2 up to the given number.

The input contains an integer n. Your task is to count how many prime numbers are present from 2 up to n, including n if it is prime.

For example, when n = 10, the prime numbers are 2, 3, 5, and 7, so the answer is 4.

Example 1
Input:
n (int) = 10
Return:
(int) 4
Example 2
Input:
n (int) = 20
Return:
(int) 8
Example 3
Input:
n (int) = 1
Return:
(int) 0

Check each number from 2 to n and count it only if it is prime.

To test whether a number is prime, try dividing it by values from 2 up to its square root. If none of those values divide it exactly, it is prime.

Pseudocode:

function countPrimeNumbersUpToN(n):
    count = 0
    for number from 2 to n:
        if isPrime(number):
            count++
    return count
function isPrime(number):
    if number <= 1:
        return false
    divisor = 2
    while divisor * divisor <= number:
        if number % divisor == 0:
            return false
        divisor++
    return true
Run your code to see the result.