Question

Write a python 3 program to generate a list of the prime numbers less than 50000 using the Sieve of Eratosthenes.

Answer 1

Complete Python Program Code For Printing Prime Numbers < 50000 Using Sieve of Eratosthenes Approach

# Given below is the Sieve of Eratosthenes function for printing all the prime numbers

# less than or equal to a given number 'n' , which in this case is 50000

def sieveOfEratosthenes(n):

    

# In this funciton we first create a boolean array named primeNumbers

# having indices from [0 to n] (both inclusive). This array will represent

# whether the number at any index 'i' is prime or not (i.e. true or false)

# we first initialise all members as True (assuming that all numbers are prime by default)

    primeNumbers = [True for k in range(n + 1)]

    j = 2 # we start with the number 2 since we already know that 0 and 1 are not prime numbers

    while (j * j <= n): # looping while square of the current number that we're checking for is <= our limit (n)

        

        # Now if the current number is still True (i.e. it is prime) then all its next multiples cannot be prime, so we make them False

        if (primeNumbers[j] == True):

            

            # Looping through all multiples of 'j' and making them False as they cannot be prime (j will divide all of them)

            for s in range(j * 2, n + 1, j):

                primeNumbers[s] = False

        j += 1 # Incrementing current 'j' by 1 so as to go to the next number for checking

    primeNumbers[0]= False # Also, at the end, since we know that 0 and 1 are not prime numbers, we make them as False explicitly

    primeNumbers[1]= False

    

# Finally in the same function, we can print all the prime numbers less than input value (n)

    for q in range(n + 1):

        if primeNumbers[q]:

            print (q)

# This below is going to be our Main function (driver code) from where we call the Sieve of Eratosthenes method

n = 50000

print ("All the Prime numbers less than or equal to the given value (",n,") are as follows:- ")

sieveOfEratosthenes(n)

URL Link To Access The Complete Above Code As It Is

https://ide.codingblocks.com/s/183165

Output Screenshots of the Program Result