Python/project_euler/problem_007/sol3.py

"""
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() = }")