Goldbach Conjecture in Python (complete, including tests)

"""
   Numerical solution to Goldbach’s conjecture.

   Author: Helton Carlos de Souza <heltoncarlossouza@hotmail.com>

   The Goldbach’s Conjecture:
   1) Every even number greater than 2 is the sum of two primes
   2) Every odd number greater than 5 is the sum of three primes.
"""


def divisors(n):
    """
        Return a divisors list of a number
        Ex.: Divisors of 12 == [1, 2, 3, 4, 6, 12]
    """
    return [x for x in range(1, n + 1) if n % x == 0]


def is_prime(n):
    """
        Check if a number is prime (a prime number has as divisors only 1 and itself)
    """
    return divisors(n) == [1, n]


def prime_range(n):
    """
        Return a list of prime numbers from 2 for n
    """
    return [x for x in range(2, n + 1) if is_prime(x)]


def goldbach_conjecture(n):
    """
        Goldbach’s conjecture numerical solution

        Input  => n:  A integer value
        Return => List of tuples (the sum of these numbers is equal to the input n):
                  The size of tuples in returned list is equal 2 (to even numbers > 2) or 3 (to odd numbers > 5)
                  Obs.: The repeated pairs are removed. For instance, 8 = 3 + 5 or 5 + 3. To more readable answer, the last pair is removed, so 8 = 3 + 5
    """
    if n % 2 == 0:
        if n > 2:
            return [(x, y) for x in prime_range(n) for y in prime_range(n) if x + y == n and x <= y]
        else:
            raise ValueError('Even numbers must be greater than 2')
    else:
        if n > 5:
            return [(x, y, z) for x in prime_range(n) for y in prime_range(n) for z in prime_range(n) if x + y + z == n and x <= y <= z]
        else:
            raise ValueError('Odd numbers must be greater than 5')


def show_goldbach_conjecture(n):
    """
        Show the goldbach_conjecture result in a "more friendly way"
    """
    tuples_list = goldbach_conjecture(n)
    print(str(n), end='')
    for t in tuples_list:
        print(" = ", end='')
        for index, number in enumerate(t):
            if index == len(t) - 1:
                print(str(number), end='')
            else:
                print(str(number) + " + ", end='')
    print()


def test(number, expected):
    """
        Test if expected value is equal to the returned value in goldbach_conjecture() function
    """
    returned = goldbach_conjecture(number)
    if returned == expected:
        prefix = ' OK '
    else:
        prefix = 'FAIL'
    print('%4s [Number = %4d] returned: %s expected: %s' % (prefix, number, repr(returned), repr(expected)))
    print('-' * 100)


def run_tests():
    """
        Automated tests for goldbach_conjecture() function
    """
    print ("Testing goldbach_conjecture() function...")
    test(6,    [(3, 3)])
    test(7,    [(2, 2, 3)])
    test(8,    [(3, 5)])
    test(9,    [(2, 2, 5), (3, 3, 3)])
    test(10,   [(3, 7), (5, 5)])
    test(11,   [(2, 2, 7), (3, 3, 5)])
    test(12,   [(5, 7)])
    test(13,   [(3, 3, 7), (3, 5, 5)])
    test(14,   [(3, 11), (7, 7)])
    test(15,   [(2, 2, 11), (3, 5, 7), (5, 5, 5)])
    test(42,   [(5, 37), (11, 31), (13, 29), (19, 23)])
    test(100,  [(3, 97), (11, 89), (17, 83), (29, 71), (41, 59), (47, 53)])
    test(150,  [(11, 139), (13, 137), (19, 131), (23, 127), (37, 113), (41, 109), (43, 107), (47, 103), (53, 97), (61, 89), (67, 83), (71, 79)])
    test(200,  [(3, 197), (7, 193), (19, 181), (37, 163), (43, 157), (61, 139), (73, 127), (97, 103)])
    test(1000, [(3, 997), (17, 983), (23, 977), (29, 971), (47, 953), (53, 947), (59, 941), (71, 929), (89, 911), (113, 887), (137, 863), (173, 827), (179, 821), (191, 809), (227, 773), (239, 761), (257, 743), (281, 719), (317, 683), (347, 653), (353, 647), (359, 641), (383, 617), (401, 599), (431, 569), (443, 557), (479, 521), (491, 509)])

if __name__ == '__main__':
    run_tests()

"""
   Using Python interpreter...

   >> from goldbach_conjecture import goldbach_conjecture, show_goldbach_conjecture
   >> goldbach_conjecture(42)
   [(5, 37), (11, 31), (13, 29), (19, 23)]
   >> show_goldbach_conjecture(42)
   42 = 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23
"""