sol2.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
"""

importmath
fromcollections.abcimportIterator
fromitertoolsimporttakewhile


defis_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
 """

if1<number<4:
# 2 and 3 are primes
returnTrue
elifnumber<2ornumber%2==0ornumber%3==0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
returnFalse

# All primes number are in format of 6k +/- 1
foriinrange(5, int(math.sqrt(number) +1), 6):
ifnumber%i==0ornumber% (i+2) ==0:
returnFalse
returnTrue


defprime_generator() ->Iterator[int]:
"""
 Generate a list sequence of prime numbers
 """

num=2
whileTrue:
ifis_prime(num):
yieldnum
num+=1


defsolution(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
 """

returnsum(takewhile(lambdax: x<n, prime_generator()))


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