project_euler.problem_077.sol1
==============================

.. py:module:: project_euler.problem_077.sol1

.. autoapi-nested-parse::

   Project Euler Problem 77: https://projecteuler.net/problem=77

   It is possible to write ten as the sum of primes in exactly five different ways:

   7 + 3
   5 + 5
   5 + 3 + 2
   3 + 3 + 2 + 2
   2 + 2 + 2 + 2 + 2

   What is the first value which can be written as the sum of primes in over
   five thousand different ways?



Attributes
----------

.. autoapisummary::

   project_euler.problem_077.sol1.NUM_PRIMES
   project_euler.problem_077.sol1.prime
   project_euler.problem_077.sol1.primes


Functions
---------

.. autoapisummary::

   project_euler.problem_077.sol1.partition
   project_euler.problem_077.sol1.solution


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

.. py:function:: partition(number_to_partition: int) -> set[int]

   Return a set of integers corresponding to unique prime partitions of n.
   The unique prime partitions can be represented as unique prime decompositions,
   e.g. (7+3) <-> 7*3 = 12, (3+3+2+2) = 3*3*2*2 = 36
   >>> partition(10)
   {32, 36, 21, 25, 30}
   >>> partition(15)
   {192, 160, 105, 44, 112, 243, 180, 150, 216, 26, 125, 126}
   >>> len(partition(20))
   26


.. py:function:: solution(number_unique_partitions: int = 5000) -> int | None

   Return the smallest integer that can be written as the sum of primes in over
   m unique ways.
   >>> solution(4)
   10
   >>> solution(500)
   45
   >>> solution(1000)
   53


.. py:data:: NUM_PRIMES
   :value: 100


.. py:data:: prime
   :type:  int

.. py:data:: primes