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Answer:
I am writing a Python program:
def Eratosthenes(n):
primeNo = [True for i in range(n+1)] # this is a boolean array
p = 2 # the first prime number is initialized as 2
while (p * p <= n): # enumerates all multiples of p
if (primeNo[p] == True):
for i in range(p * p, n+1, p): #update multiples
primeNo[i] = False
p = p + 1
for p in range(2, n): #display all the prime numbers
if primeNo[p]:
print(p),
def main(): #to take value of n from user and display prime numbers #less than or equal to n by calling Eratosthenes method
n= int(input("Enter an integer n: "))
print("The prime numbers less than or equal to",n, "are: ")
Eratosthenes(n)
main()
Explanation:
The program contains a Boolean type array primeNo that is initialized by True which means that any value i in prime array will be true if i is a prime otherwise it will be false. The while loop keeps enumerating all multiples of p starting from 2, and striking them off from the original array list and for loops keep updating the multiples. This process will continue till the p is greater than n. The last for loop displays all the prime numbers less than or equal to n which is input by user. main() function prompts user to enter the value of integer n and then calls Eratosthenes() function to print all the prime numbers less than or equal to a given integer n.
