mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 09:10:16 +00:00
2104fa7aeb
* fixes #5434 * fixes broken solution * removes assert * removes assert * Apply suggestions from code review Co-authored-by: John Law <johnlaw.po@gmail.com> * Update project_euler/problem_003/sol1.py Co-authored-by: John Law <johnlaw.po@gmail.com>
83 lines
1.8 KiB
Python
83 lines
1.8 KiB
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() = }")
|