project_euler.problem_050.sol1
==============================

.. py:module:: project_euler.problem_050.sol1

.. autoapi-nested-parse::

   Project Euler Problem 50: https://projecteuler.net/problem=50

   Consecutive prime sum

   The prime 41, can be written as the sum of six consecutive primes:
   41 = 2 + 3 + 5 + 7 + 11 + 13

   This is the longest sum of consecutive primes that adds to a prime below
   one-hundred.

   The longest sum of consecutive primes below one-thousand that adds to a prime,
   contains 21 terms, and is equal to 953.

   Which prime, below one-million, can be written as the sum of the most
   consecutive primes?



Functions
---------

.. autoapisummary::

   project_euler.problem_050.sol1.prime_sieve
   project_euler.problem_050.sol1.solution


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

.. py:function:: prime_sieve(limit: int) -> list[int]

   Sieve of Erotosthenes
   Function to return all the prime numbers up to a number 'limit'
   https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

   >>> prime_sieve(3)
   [2]

   >>> prime_sieve(50)
   [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]


.. py:function:: solution(ceiling: int = 1000000) -> int

   Returns the biggest prime, below the celing, that can be written as the sum
   of consecutive the most consecutive primes.

   >>> solution(500)
   499

   >>> solution(1_000)
   953

   >>> solution(10_000)
   9521