project_euler.problem_187.sol1
==============================

.. py:module:: project_euler.problem_187.sol1

.. autoapi-nested-parse::

   Project Euler Problem 187: https://projecteuler.net/problem=187

   A composite is a number containing at least two prime factors.
   For example, 15 = 3 x 5; 9 = 3 x 3; 12 = 2 x 2 x 3.

   There are ten composites below thirty containing precisely two,
   not necessarily distinct, prime factors: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

   How many composite integers, n < 10^8, have precisely two,
   not necessarily distinct, prime factors?



Functions
---------

.. autoapisummary::

   project_euler.problem_187.sol1.benchmark
   project_euler.problem_187.sol1.calculate_prime_numbers
   project_euler.problem_187.sol1.slow_calculate_prime_numbers
   project_euler.problem_187.sol1.slow_solution
   project_euler.problem_187.sol1.solution
   project_euler.problem_187.sol1.while_solution


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

.. py:function:: benchmark() -> None

   Benchmarks


.. py:function:: calculate_prime_numbers(max_number: int) -> list[int]

   Returns prime numbers below max_number.
   See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

   >>> calculate_prime_numbers(10)
   [2, 3, 5, 7]

   >>> calculate_prime_numbers(2)
   []


.. py:function:: slow_calculate_prime_numbers(max_number: int) -> list[int]

   Returns prime numbers below max_number.
   See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

   >>> slow_calculate_prime_numbers(10)
   [2, 3, 5, 7]

   >>> slow_calculate_prime_numbers(2)
   []


.. py:function:: slow_solution(max_number: int = 10**8) -> int

   Returns the number of composite integers below max_number have precisely two,
   not necessarily distinct, prime factors.

   >>> slow_solution(30)
   10


.. py:function:: solution(max_number: int = 10**8) -> int

   Returns the number of composite integers below max_number have precisely two,
   not necessarily distinct, prime factors.

   >>> solution(30)
   10


.. py:function:: while_solution(max_number: int = 10**8) -> int

   Returns the number of composite integers below max_number have precisely two,
   not necessarily distinct, prime factors.

   >>> while_solution(30)
   10