""" 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 """ from maths.prime_check import is_prime def 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 """ if not isinstance(number, int) or number < 1: msg = f"Input value must be a positive integer. Input value: {number}" raise TypeError(msg) return is_prime(number) and is_prime(2 * number + 1) def 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 """ if not isinstance(number, int) or number < 1: msg = f"Input value must be a positive integer. Input value: {number}" raise TypeError(msg) return (number - 1) % 2 == 0 and is_prime(number) and is_prime((number - 1) // 2) if __name__ == "__main__": from doctest import testmod testmod()