High School

a) Create a recursive function structure to calculate and print the cumulative sum of the prime numbers between 1 and 20000 at each step.

b) Find how many prime numbers there are between 1 and 20000.

Answer :

Final answer:

To create a recursive function structure to calculate and print the cumulative sum of prime numbers between 1 and 20000, follow these steps: create a recursive function to check if a number is prime, iterate through the numbers, check if the number is prime, add it to the cumulative sum, print the sum, and finally print the total count of prime numbers.

Explanation:

To create a recursive function structure to calculate and print the cumulative sum of prime numbers between 1 and 20000, you can follow these steps:

  1. Create a recursive function that checks if a number is prime or not.
  2. Initialize a variable to store the cumulative sum.
  3. Iterate through the numbers from 1 to 20000.
  4. In each iteration, check if the number is prime using the recursive function.
  5. If the number is prime, add it to the cumulative sum and print the updated sum.
  6. After the loop ends, print the total count of prime numbers.

Example:

def is_ prime(n):

if n > 20000:

current_ sum += n

cumulative_ prime_ sum(n+1, current_ sum)

cumulative_ prime_ sum(1, 0)

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Final answer:

To calculate and print the cumulative sum of prime numbers between 1 and 20000, you can create a recursive function that checks if a number is prime and adds it to a running total. The function can be implemented in Python as shown above.

Explanation:

To create a recursive function structure to calculate and print the cumulative sum of prime numbers between 1 and 20000, you can define a function that checks whether a number is prime or not. Start with the number 2 and iterate through each number up to 20000. If a number is prime, add it to a running total and print the sum at each step.



Here's an example of how the recursive function can be implemented in Python:




prime_sum = 0

# Recursive function to check if a number is prime

def is_prime(n):
if n == 2:
return True
if n < 2 or n % 2 == 0:
return False
for i in range(3, int(n ** 0.5) + 1, 2):
if n % i == 0:
return False
return True

# Recursive function to calculate and print cumulative sum of prime numbers


def cumulative_prime_sum(n):
global prime_sum
if n < 2:
return
if is_prime(n):
prime_sum += n
print(prime_sum)
cumulative_prime_sum(n - 1)

cumulative_prime_sum(20000)



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