maths.germain_primes
====================

.. py:module:: maths.germain_primes

.. autoapi-nested-parse::

   A Sophie Germain prime is any prime p, where 2p + 1 is also prime.
   The second number, 2p + 1 is called a safe prime.

   Examples of Germain primes include: 2, 3, 5, 11, 23

   Their corresponding safe primes: 5, 7, 11, 23, 47
   https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes



Functions
---------

.. autoapisummary::

   maths.germain_primes.is_germain_prime
   maths.germain_primes.is_safe_prime


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

.. py:function:: is_germain_prime(number: int) -> bool

   Checks if input number and 2*number + 1 are prime.

   >>> is_germain_prime(3)
   True
   >>> is_germain_prime(11)
   True
   >>> is_germain_prime(4)
   False
   >>> is_germain_prime(23)
   True
   >>> is_germain_prime(13)
   False
   >>> is_germain_prime(20)
   False
   >>> is_germain_prime('abc')
   Traceback (most recent call last):
       ...
   TypeError: Input value must be a positive integer. Input value: abc


.. py:function:: is_safe_prime(number: int) -> bool

   Checks if input number and (number - 1)/2 are prime.
   The smallest safe prime is 5, with the Germain prime is 2.

   >>> is_safe_prime(5)
   True
   >>> is_safe_prime(11)
   True
   >>> is_safe_prime(1)
   False
   >>> is_safe_prime(2)
   False
   >>> is_safe_prime(3)
   False
   >>> is_safe_prime(47)
   True
   >>> is_safe_prime('abc')
   Traceback (most recent call last):
       ...
   TypeError: Input value must be a positive integer. Input value: abc