project_euler.problem_111.sol1
==============================

.. py:module:: project_euler.problem_111.sol1

.. autoapi-nested-parse::

   Project Euler Problem 111: https://projecteuler.net/problem=111

   Primes with Runs

   First, note that for sequence of 10 digits, M(4,d) is 8 or 9.
   Start by constructing prime list up to sqrt(n), which are used to check if
   number is prime.
   Then iterate over possible combinations of numbers checking each if prime.



Functions
---------

.. autoapisummary::

   project_euler.problem_111.sol1.generate_primes
   project_euler.problem_111.sol1.is_prime
   project_euler.problem_111.sol1.solution


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

.. py:function:: generate_primes(n: int)

   Calculates the list of primes up to and including n.

   >>> generate_primes(6)
   [2, 3, 5]


.. py:function:: is_prime(n, primes_all)

   Check in int n is prime using primes_all list of relatively small primes
   compared to n.

   >>> is_prime(5, [2, 3])
   True


.. py:function:: solution(n: int = 10000000000) -> int

   Check each possible combination if it is prime.


   >>> solution(10000)
   273700