Python Programs to Find Sum of First n Prime Numbers

A Prime Number is a number that can only be divided by itself and 1 without remainders (e.g., 2, 3, 5, 7, 11). There are two ways to find the sum of the first n prime numbers between 1 and n using Python.

To solve this problem you need to know how to use the below concepts.

• for loop, range() function and while loop
• if-else condition
• Math module

1. Using loop

We can use for loop to calculate the sum of the first n prime numbers by iterating through numbers from 1 to n, checking if they are prime, and summing them.

Also, see:

• Python Programs to Check if Number is Prime Number
• Python Programs to Find Prime Numbers within a Range

Code Example: Calculate the sum of first 5 prime numbers.

import math

def is_prime(num):
    if num <= 1:
        return False
    for i in range(2, int(math.sqrt(num)) + 1):  # optimized by the checking till √n
        if num % i == 0:
            return False
    return True

n = 4   # first 5 prime numbers
prime_sum = 0   # sum of prime numbers
prime_counter = 0 # counter of prime numbers 
num = 2  # Start from the first prime number
while prime_counter < n:
    if is_prime(num):
        print(num)
        prime_sum += num
        prime_counter += 1 
    num += 1
print(f"The sum of the first {n} prime numbers is: {prime_sum}")Code language: Python (python)

Output:

2
3
5
7
11
The sum of the first 4 prime numbers is: 28

Explanation

• We are using a while loop to iterate over numbers starting from 2 until we get the expected number of prime numbers, which is 5 in this case.
• In each iteration of a loop, we are doing the following operation:
  1. Checking if the number is prime using is_prime() function
  2. Printing the number if its prime
  3. Summing it with prime_sum
  4. Incrementing the prime number counter (prime_counter) by 1
  5. Increment the number by 1 to get the next number in the series, i.e., 3, 4, and so on…
  6. Iteration ends when prime_counter reaches the expected prime number count.
• is_prime(): It is a function to find the prime number, we check divisibility num % i == 0 only up to the square root of the number, which significantly improves performance.
  • Edge case: Numbers less than or equal to 1 are immediately classified as not prime because prime numbers are greater than 1.
  • Use of math.sqrt: The math.sqrt function calculates the square root of n.
  • for Loop: The loop iterates from 2 up to and including √n, significantly reducing the number of checks needed compared to iterating through all numbers up to n-1.
  • Modulo operator (%): The modulo operator is used to check divisibility. If n % i == 0, then i is a divisor of n, indicating that the number is not prime.

2. Using Python’s Built-in filter() and itertools

Code Example

import math
import itertools

def is_prime(num):
    if num <= 1:
        return False
    for i in range(2, int(math.sqrt(num)) + 1):  # optimized by the checking till √n
        if num % i == 0:
            return False
    return True

n = 4
primes = filter(is_prime, itertools.count(2))  # Infinite generator of prime numbers
prime_sum = sum(itertools.islice(primes, n))
print(f"The sum of the first {n} prime numbers is: {prime_sum}")Code language: Python (python)

Output:

The sum of the first 4 prime numbers is: 17Code language: Python (python)