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Python Math: Print all primes (Sieve of Eratosthenes) smaller than or equal to a specified number

Python Math: Exercise-21 with Solution

Write a Python program to print all primes (Sieve of Eratosthenes) smaller than or equal to a specified number.

In mathematics, the sieve of Eratosthenes, one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the multiples of 2.

Pictorial presentation:

Sieve_of_Eratosthenes

Animation Credits: Author information here

Sample Solution:-

Python Code:


def sieve_of_Eratosthenes(num):
    limitn = num+1
    not_prime_num = set()
    prime_nums = []

    for i in range(2, limitn):
        if i in not_prime_num:
            continue

        for f in range(i*2, limitn, i):
            not_prime_num.add(f)

        prime_nums.append(i)

    return prime_nums

print(sieve_of_Eratosthenes(100));

Sample Output: 

[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]

Flowchart:

Flowchart: Print all primes (Sieve of Eratosthenes) smaller than or equal to a specified number

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Previous: Write a Python program to calculate magic square.
Next: Write a python program to find the next smallest palindrome of a specified number.

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

  • The os and os.path modules.
  • The __file__ constant
  • os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
  • os.path.dirname(path) (returns "the directory name of pathname path")
  • os.getcwd() (returns "a string representing the current working directory")
  • os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m