sieve_of_eratosthenes.py

"""
Sieve of Eratosthones

The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or
equal to a given value.
Illustration:
https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

doctest provider: Bruno Simas Hadlich (https://github.com/brunohadlich)
Also thanks to Dmitry (https://github.com/LizardWizzard) for finding the problem
"""

from __future__ importannotations

importmath


defprime_sieve(num: int) ->list[int]:
"""
 Returns a list with all prime numbers up to n.

 >>> prime_sieve(50)
 [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
 >>> prime_sieve(25)
 [2, 3, 5, 7, 11, 13, 17, 19, 23]
 >>> prime_sieve(10)
 [2, 3, 5, 7]
 >>> prime_sieve(9)
 [2, 3, 5, 7]
 >>> prime_sieve(2)
 [2]
 >>> prime_sieve(1)
 []
 """

ifnum<=0:
msg=f"{num}: Invalid input, please enter a positive integer."
raiseValueError(msg)

sieve= [True] * (num+1)
prime= []
start=2
end=int(math.sqrt(num))

whilestart<=end:
# If start is a prime
ifsieve[start] isTrue:
prime.append(start)

# Set multiples of start be False
foriinrange(start*start, num+1, start):
ifsieve[i] isTrue:
sieve[i] =False

start+=1

forjinrange(end+1, num+1):
ifsieve[j] isTrue:
prime.append(j)

returnprime


if__name__=="__main__":
print(prime_sieve(int(input("Enter a positive integer: ").strip())))