Python/project_euler/problem_10/sol3.py

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"""
https://projecteuler.net/problem=10
Problem Statement:
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
"""
def solution(n: int = 2000000) -> int:
"""Returns the sum of all the primes below n using Sieve of Eratosthenes:
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
The sieve of Eratosthenes is one of the most efficient ways to find all primes
smaller than n when n is smaller than 10 million. Only for positive numbers.
>>> solution(2_000_000)
142913828922
>>> solution(1_000)
76127
>>> solution(5_000)
1548136
>>> solution(10_000)
5736396
>>> solution(7)
10
>>> solution(7.1) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
>>> solution(-7) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
IndexError: list assignment index out of range
>>> solution("seven") # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: can only concatenate str (not "int") to str
"""
primality_list = [0 for i in range(n + 1)]
primality_list[0] = 1
primality_list[1] = 1
for i in range(2, int(n ** 0.5) + 1):
if primality_list[i] == 0:
for j in range(i * i, n + 1, i):
primality_list[j] = 1
sum_of_primes = 0
for i in range(n):
if primality_list[i] == 0:
sum_of_primes += i
return sum_of_primes
if __name__ == "__main__":
print(solution(int(input().strip())))