project_euler.problem_046.sol1
==============================

.. py:module:: project_euler.problem_046.sol1

.. autoapi-nested-parse::

   Problem 46: https://projecteuler.net/problem=46

   It was proposed by Christian Goldbach that every odd composite number can be
   written as the sum of a prime and twice a square.

   9 = 7 + 2 x 12
   15 = 7 + 2 x 22
   21 = 3 + 2 x 32
   25 = 7 + 2 x 32
   27 = 19 + 2 x 22
   33 = 31 + 2 x 12

   It turns out that the conjecture was false.

   What is the smallest odd composite that cannot be written as the sum of a
   prime and twice a square?



Attributes
----------

.. autoapisummary::

   project_euler.problem_046.sol1.odd_composites


Functions
---------

.. autoapisummary::

   project_euler.problem_046.sol1.compute_nums
   project_euler.problem_046.sol1.is_prime
   project_euler.problem_046.sol1.solution


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

.. py:function:: compute_nums(n: int) -> list[int]

   Returns a list of first n odd composite numbers which do
   not follow the conjecture.
   >>> compute_nums(1)
   [5777]
   >>> compute_nums(2)
   [5777, 5993]
   >>> compute_nums(0)
   Traceback (most recent call last):
       ...
   ValueError: n must be >= 0
   >>> compute_nums("a")
   Traceback (most recent call last):
       ...
   ValueError: n must be an integer
   >>> compute_nums(1.1)
   Traceback (most recent call last):
       ...
   ValueError: n must be an integer



.. 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.

   >>> is_prime(0)
   False
   >>> is_prime(1)
   False
   >>> is_prime(2)
   True
   >>> is_prime(3)
   True
   >>> is_prime(27)
   False
   >>> is_prime(87)
   False
   >>> is_prime(563)
   True
   >>> is_prime(2999)
   True
   >>> is_prime(67483)
   False


.. py:function:: solution() -> int

   Return the solution to the problem


.. py:data:: odd_composites