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Print Prime Numbers in a Given Range

Certification: Basic Level Accuracy: 55.36% Submissions: 56 Points: 10

Write a Python program that prints all prime numbers within a given range from start to end (inclusive).

Example 1
    

  • Input: start = 10, end = 20
    • 

  • Output: [11, 13, 17, 19]
    • 

  • Explanation: 
      

    • Step 1: For each number from 10 to 20, check 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: 11, 13, 17, and 19 are prime because they have no divisors other than 1 and themselves.
      • 

    • Step 4: Return the list of prime numbers found in the range.
      • 

    •
Example 2
    

  • Input: start = 30, end = 40
    • 

  • Output: [31, 37]
    • 

  • Explanation: 
      

    • Step 1: For each number from 30 to 40, check 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: 31 and 37 are prime because they have no divisors other than 1 and themselves.
      • 

    • Step 4: Return the list of prime numbers found in the range.
      • 

    •
Constraints
    

  • 1 ≤ start ≤ end ≤ 10^5
    • 

  • Time Complexity: O(n * sqrt(n)) where n is the size of the range
    • 

  • Space Complexity: O(k) where k is the number of prime numbers in the range
    •
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Hint
Solution

Solution Hints

    
  
  • Use a helper function to check if a number is prime
    • 
  
  • A number is prime if it is not divisible by any integer from 2 to sqrt(n)
    • 
  
  • Optimize by checking only odd numbers after 2
    •

Steps to solve by this approach:

 Step 1: Define a nested helper function to check if a number is prime.

 Step 2: In the helper function, handle edge cases and use optimized primality testing.

 Step 3: Initialize an empty list to store prime numbers found.

 Step 4: Iterate through each number in the specified range (inclusive).

 Step 5: Use list comprehension to filter numbers that are prime according to the helper function.

 Step 6: Return the list of prime numbers found in the range.

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