project euler problem 7 https projecteuler netproblem7 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 orgwikiprimenumber checks to see if a number is a prime in osqrtn a number is prime if it has exactly two factors 1 and itself returns boolean representing primality of given number i e if the result is true then the number is indeed prime else it is not isprime2 true isprime3 true isprime27 false isprime2999 true isprime0 false isprime1 false 2 and 3 are primes negatives 0 1 all even numbers all multiples of 3 are not primes all primes number are in format of 6k 1 returns the nth prime number solution6 13 solution1 2 solution3 5 solution20 71 solution50 229 solution100 541 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 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 2 and 3 are primes negatives 0 1 all even numbers all multiples of 3 are not primes all primes number are in format of 6k 1 returns the n th prime number solution 6 13 solution 1 2 solution 3 5 solution 20 71 solution 50 229 solution 100 541
from math import sqrt


def is_prime(number: int) -> bool:
    

    if 1 < number < 4:
        
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        
        return False

    
    for i in range(5, int(sqrt(number) + 1), 6):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True


def solution(nth: int = 10001) -> int:
    

    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(f"{solution() = }")