project_euler.problem_037.sol1
==============================

.. py:module:: project_euler.problem_037.sol1

.. autoapi-nested-parse::

   Truncatable primes
   Problem 37: https://projecteuler.net/problem=37

   The number 3797 has an interesting property. Being prime itself, it is possible
   to continuously remove digits from left to right, and remain prime at each stage:
   3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

   Find the sum of the only eleven primes that are both truncatable from left to right
   and right to left.

   NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.



Functions
---------

.. autoapisummary::

   project_euler.problem_037.sol1.compute_truncated_primes
   project_euler.problem_037.sol1.is_prime
   project_euler.problem_037.sol1.list_truncated_nums
   project_euler.problem_037.sol1.solution
   project_euler.problem_037.sol1.validate


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

.. py:function:: compute_truncated_primes(count: int = 11) -> list[int]

   Returns the list of truncated primes
   >>> compute_truncated_primes(11)
   [23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397]


.. 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:: list_truncated_nums(n: int) -> list[int]

   Returns a list of all left and right truncated numbers of n
   >>> list_truncated_nums(927628)
   [927628, 27628, 92762, 7628, 9276, 628, 927, 28, 92, 8, 9]
   >>> list_truncated_nums(467)
   [467, 67, 46, 7, 4]
   >>> list_truncated_nums(58)
   [58, 8, 5]


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

   Returns the sum of truncated primes


.. py:function:: validate(n: int) -> bool

   To optimize the approach, we will rule out the numbers above 1000,
   whose first or last three digits are not prime
   >>> validate(74679)
   False
   >>> validate(235693)
   False
   >>> validate(3797)
   True