Python/project_euler/problem_007/sol3.py

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"""
Project Euler Problem 7: https://projecteuler.net/problem=7
10001st prime
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
can see that the 6th prime is 13.
What is the 10001st prime number?
References:
- https://en.wikipedia.org/wiki/Prime_number
"""
import itertools
import math
def is_prime(number: int) -> bool:
"""
Determines whether a given number is prime or not
>>> is_prime(2)
True
>>> is_prime(15)
False
>>> is_prime(29)
True
"""
if number % 2 == 0 and number > 2:
return False
return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))
def prime_generator():
"""
Generate a sequence of prime numbers
"""
num = 2
while True:
if is_prime(num):
yield num
num += 1
def solution(nth: int = 10001) -> int:
"""
Returns the n-th prime number.
>>> solution(6)
13
>>> solution(1)
2
>>> solution(3)
5
>>> solution(20)
71
>>> solution(50)
229
>>> solution(100)
541
"""
return next(itertools.islice(prime_generator(), nth - 1, nth))
if __name__ == "__main__":
print(f"{solution() = }")