germain_primes.py

"""
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
"""

frommaths.prime_checkimportis_prime


defis_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
 """
ifnotisinstance(number, int) ornumber<1:
msg=f"Input value must be a positive integer. Input value: {number}"
raiseTypeError(msg)

returnis_prime(number) andis_prime(2*number+1)


defis_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
 """
ifnotisinstance(number, int) ornumber<1:
msg=f"Input value must be a positive integer. Input value: {number}"
raiseTypeError(msg)

return (number-1) %2==0andis_prime(number) andis_prime((number-1) //2)


if__name__=="__main__":
fromdoctestimporttestmod

testmod()