Count Primes in Python

Suppose we have a limit n. We have to count the number of primes present in the range 2 to n. So if n = 10, the result will be 4. As there are four primes before 10, they are 2, 3, 5, 7.

To solve this, we will follow this approach −

• count = 0
• take one array prime = of size n + 1, and fill it with False
• for i = 0 to n, do
  • if prime[i] = false, then
    • increase count by 1
    • set j = 2
    • while j * i <n, then
      • prime[i * j] = True
      • j = j + 1
• return count

Example

Let us see the following implementation to get a better understanding −

 Live Demo

class Solution(object):
   def countPrimes(self, n):
      """
      :type n: int
      :rtype: int
      """
      count = 0
      primes = [False for i in range(n+1)]
      for i in range(2,n):
         if primes[i] == False:
            count+=1
            j = 2
            while j*i<n:
               primes[j*i] = True
               j+=1
      return count
ob1 = Solution()
print(ob1.countPrimes(50))
print(ob1.countPrimes(10))

Input

n = 50
n = 10

Output

15
4