project_euler.problem_007.sol1
==============================

.. py:module:: project_euler.problem_007.sol1

.. autoapi-nested-parse::

   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



Functions
---------

.. autoapisummary::

   project_euler.problem_007.sol1.is_prime
   project_euler.problem_007.sol1.solution


Module Contents
---------------

.. py:function:: is_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 (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


.. py:function:: 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