How to Check if a Number is Prime in Python?

[Ackbach]

Here is this week's POTW:

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Write a computer program in Python to check a positive integer for primality. You may not use any built-in primitives that look like "IsPrime(n)". Check all the numbers up to $\sqrt{n}$, and skip the evens after 2.

Inputs: integer n. Check that the input is a positive integer. If it is not an integer, return an informative error message.

Outputs: boolean IsPrime, string Error. The boolean will be TRUE if the integer is prime, and FALSE if it is not. The error string will be empty if the input is a positive integer, and will return a suitable error message if it is not.

NB: because the function must return multiple values, define a class containing all the outputs, and return that.

The program must run correctly with Python Version 3.4.

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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!

 

[Ackbach]

Congratulations to Bacterius for his correct (overliteral) solution, which I give below:

Spoiler

#!/usr/bin/env python3

# A primality test, following Ackbach's precise specifications.

class Result:
    def __init__(self, IsPrime, Error):
        self.IsPrime = IsPrime
        self.Error = Error

    @staticmethod
    def Error(msg):
        return Result(None, msg)

    @staticmethod
    def IsPrime():
        return Result(True, "")

    @staticmethod
    def IsNotPrime():
        return Result(False, "")

    def __repr__(self):
        return '(IsPrime={0}, Error="{1}")'.format(self.IsPrime,
                                                   self.Error)

def is_prime(n):
    if not isinstance(n, int):
        return Result.Error("an informative error message")

    if n <= 0:
        return Result.Error("a suitable error message")

    if n == 2:
        return Result.IsPrime()
    elif n == 1 or n % 2 == 0:
        return Result.IsNotPrime()
    else:
        divisor = 3

        while divisor * divisor <= n:
            if n % divisor == 0:
                return Result.IsNotPrime()
            else:
                divisor += 2

        return Result.IsPrime()

# PS: it isn't necessary to define a class to return multiple values in Python
#     as multiple return values are automatically packed into a tuple, e.g.:
#
#   def func():
#       return 12345, "hello"
#
#   x, y = func()
#   print(x)        (prints 12345)
#   print(y)        (prints hello)
#