Python/project_euler/problem_010/sol2.py
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Python

"""
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
"""
import math
from collections.abc import Iterator
from itertools import takewhile
def is_prime(number: int) -> bool:
"""Checks to see if a number is a prime in O(sqrt(n)).
A number is prime if it has exactly two factors: 1 and itself.
Returns boolean representing primality of given number num (i.e., if the
result is true, then the number is indeed prime else it is not).
>>> is_prime(2)
True
>>> is_prime(3)
True
>>> is_prime(27)
False
>>> is_prime(2999)
True
>>> is_prime(0)
False
>>> is_prime(1)
False
"""
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True
def prime_generator() -> Iterator[int]:
"""
Generate a list sequence of prime numbers
"""
num = 2
while True:
if is_prime(num):
yield num
num += 1
def solution(n: int = 2000000) -> int:
"""
Returns the sum of all the primes below n.
>>> solution(1000)
76127
>>> solution(5000)
1548136
>>> solution(10000)
5736396
>>> solution(7)
10
"""
return sum(takewhile(lambda x: x < n, prime_generator()))
if __name__ == "__main__":
print(f"{solution() = }")