Python/maths/prime_sieve_eratosthenes.py

"""
Sieve of Eratosthenes

Input : n =10
Output: 2 3 5 7

Input : n = 20
Output: 2 3 5 7 11 13 17 19

you can read in detail about this at
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""


def prime_sieve_eratosthenes(num):
    """
    print the prime numbers up to n

    >>> prime_sieve_eratosthenes(10)
    2,3,5,7,
    >>> prime_sieve_eratosthenes(20)
    2,3,5,7,11,13,17,19,
    """

    primes = [True for i in range(num + 1)]
    p = 2

    while p * p <= num:
        if primes[p]:
            for i in range(p * p, num + 1, p):
                primes[i] = False
        p += 1

    for prime in range(2, num + 1):
        if primes[prime]:
            print(prime, end=",")


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    num = int(input())

    prime_sieve_eratosthenes(num)