Python: Compute the sum of first n given prime numbers

Last update on May 24 2025 10:48:52 (UTC/GMT +8 hours)

Sum of First n Primes

Write a Python program to compute the sum of the first n prime numbers.

Input:
n ( n ≤ 10000). Input 0 to exit the program.
Input a number (n≤10000) to compute the sum:(0 to exit)
25
Sum of first 25 prime numbers:
1060

Visual Presentation:

Sample Solution:

Python Code:

# Set the maximum limit for prime number computation
MAX = 105000

# Print statement to prompt the user to input a number (n≤10000) to compute the sum (0 to exit)
print("Input a number (n≤10000) to compute the sum:(0 to exit)")

# Boolean list to track prime numbers using the Sieve of Eratosthenes algorithm
is_prime = [True for _ in range(MAX)]
is_prime[0] = is_prime[1] = False

# Iterate through the range to mark non-prime numbers
for i in range(2, int(MAX ** (1 / 2)) + 1):
  if is_prime[i]:
    for j in range(i ** 2, MAX, i):
      is_prime[j] = False 

# Create a list of prime numbers within the given range
primes = [i for i in range(MAX) if is_prime[i]] 

# Infinite loop to continuously accept user input until 0 is entered
while True:
  # Prompt the user to input a number
  n = int(input())
  
  # Check if the entered number is 0, and exit the loop if true
  if not n:
    break
  
  # Print statement to display the sum of the first n prime numbers
  print("Sum of first", n, "prime numbers:")
  
  # Calculate and print the sum of the first n prime numbers using list slicing
  print(sum(primes[:n]))

Sample Output:

Input a number (n≤10000) to compute the sum:(0 to exit)
 25
Sum of first 25 prime numbers:
1060

Explanation:

Here is a breakdown of the above Python code:

• First the code sets the maximum limit for prime number computation (MAX).
• It initializes a boolean list (is_prime) to track prime numbers using the Sieve of Eratosthenes algorithm.
• The code creates a list of prime numbers (primes) within the specified range.
• It enters an infinite loop to continuously accept user input until 0 is entered.
• Inside the loop, it prompts the user to input a number (n) and calculates the sum of the first n prime numbers.
• The loop exits if the entered number is 0.

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to compute the sum of the first n prime numbers using the Sieve of Eratosthenes for efficiency.
• Write a Python program to calculate the sum of the first n primes and validate the result with a recursive prime-checking function.
• Write a Python program to continuously add prime numbers until the cumulative sum exceeds a given threshold.
• Write a Python program to implement memoization in computing the sum of the first n prime numbers for repeated calls.

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Next: Write a Python program that accept a even number (>=4, Goldbach number) from the user and create a combinations that express the given number as a sum of two prime numbers. Print the number of combinations.

Python Code Editor:

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