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Count the Number of Prime Numbers in a Given Range

Certification: Basic Level Accuracy: 65% Submissions: 40 Points: 15

Write a Python program that counts the number of prime numbers within a given range.

Example 1
    

  • Input: start = 10, end = 20
    • 

  • Output: 4
    • 

  • Explanation: 
      

    • Step 1: Check each number from 10 to 20 to determine if it's prime.
      • 

    • Step 2: A number is prime if it's greater than 1 and has no divisors other than 1 and itself.
      • 

    • Step 3: Prime numbers in the range [10, 20] are: 11, 13, 17, 19.
      • 

    • Step 4: There are 4 prime numbers in this range.
      • 

    • Step 5: Return 4.
      • 

    •
Example 2
    

  • Input: start = 1, end = 10
    • 

  • Output: 4
    • 

  • Explanation: 
      

    • Step 1: Check each number from 1 to 10 to determine if it's prime.
      • 

    • Step 2: A number is prime if it's greater than 1 and has no divisors other than 1 and itself.
      • 

    • Step 3: Prime numbers in the range [1, 10] are: 2, 3, 5, 7.
      • 

    • Step 4: There are 4 prime numbers in this range.
      • 

    • Step 5: Return 4.
      • 

    •
Constraints
    

  • 1 ≤ start ≤ end ≤ 10^6
    • 

  • Time Complexity: O((end-start) * sqrt(end)) where end-start is the size of the range
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
        
  • Implement a function to check if a number is prime
    • 
        
  • For prime checking, only check divisibility up to the square root of the number
    •

Steps to solve by this approach:

 Step 1: Create a helper function to determine if a number is prime.

 Step 2: In the helper function, handle special cases (numbers <= 1 are not prime, 2 and 3 are prime).

 Step 3: Optimize primality testing using divisibility by 2, 3, and numbers of form 6k+=1.

 Step 4: Initialize a counter for prime numbers found in the range.

 Step 5: Iterate through each number in the specified range (inclusive).

 Step 6: For each number, check if it's prime using the helper function and increment the counter if true.

 Step 7: Return the final count of prime numbers in the range.

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