sol3.py

"""
Project Euler Problem 10: https://projecteuler.net/problem=10

Summation of primes

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

References:
 - https://en.wikipedia.org/wiki/Prime_number
 - https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""


defsolution(n: int=2000000) ->int:
"""
 Returns the sum of all the primes below n using 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(1000)
 76127
 >>> solution(5000)
 1548136
 >>> solution(10000)
 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= [0foriinrange(n+1)]
primality_list[0] =1
primality_list[1] =1

foriinrange(2, int(n**0.5) +1):
ifprimality_list[i] ==0:
forjinrange(i*i, n+1, i):
primality_list[j] =1
sum_of_primes=0
foriinrange(n):
ifprimality_list[i] ==0:
sum_of_primes+=i
returnsum_of_primes


if__name__=="__main__":
print(f"{solution() =}")