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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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Next: Write a python program to find the next smallest palindrome of a specified number.

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