maths.germain_primes

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

is_germain_prime(→ bool)	Checks if input number and 2*number + 1 are prime.
is_safe_prime(→ bool)	Checks if input number and (number - 1)/2 are prime.

Module Contents

maths.germain_primes.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

maths.germain_primes.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