Python/project_euler/problem_007/sol1.py

"""
Problem 7: https://projecteuler.net/problem=7

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 Nth prime number?
"""
from math import sqrt


def is_prime(num: int) -> bool:
    """Determines whether the given number is prime or not"""
    if num == 2:
        return True
    elif num % 2 == 0:
        return False
    else:
        sq = int(sqrt(num)) + 1
        for i in range(3, sq, 2):
            if num % i == 0:
                return False
    return True


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
    >>> solution()
    104743
    """
    count = 0
    number = 1
    while count != nth and number < 3:
        number += 1
        if is_prime(number):
            count += 1
    while count != nth:
        number += 2
        if is_prime(number):
            count += 1
    return number


if __name__ == "__main__":
    print(solution(int(input().strip())))