def test_is_prime_false_for_any_integer_not_ending_in_1379(z):
if z <= 1:
assert not is_prime(z)
elif z == 2:
assert is_prime(z)
else:
if str(z)[-1] not in map(str, (1, 3, 7, 9)):
assert not is_prime(z)
def test_goldbach_partitions(z):
expected = set()
if z % 2:
assert Integer(z).goldbach_partitions == expected
else:
expected = set(filter(lambda x: is_prime(x[0]) and is_prime(x[1]),
zip(range(z//2+1),
(z - x for x in range(z//2+1)))))
assert Integer(z).goldbach_partitions == expected
def test_nearest_prime(z):
def generate_primes_before_n(n):
p = generate_primes()
largest_so_far = next(p)
while largest_so_far < n:
yield largest_so_far
largest_so_far = next(p)
def generate_primes_after_n(n):
p = generate_primes()
largest_so_far = next(p)
while largest_so_far < n:
largest_so_far = next(p)
yield largest_so_far
while True:
yield next(p)
np = Integer(z).nearest_prime
if z <= 0:
assert np == (2,)
elif is_prime(z):
assert np == (z,)
else:
closest_before_z = max(generate_primes_before_n(z))
closest_after_z = next(generate_primes_after_n(z))
if abs(z - closest_before_z) == abs(z - closest_after_z):
assert np == (closest_before_z, closest_after_z)
else:
assert np == (min(closest_after_z, closest_before_z,
key=lambda n, z=z: abs(z-n)),)
def test_is_mersenne_prime(z):
if z <= 0:
assert not Integer(z).is_mersenne_prime
else:
if math.log(z+1, 2).is_integer() and is_prime(z):
assert Integer(z).is_mersenne_prime
else:
assert not Integer(z).is_mersenne_prime
def test_primality(z):
if is_prime(z):
assert Integer(z).primality == "Prime"
else:
assert Integer(z).primality == "Composite"
def test_pi(z):
assert Integer(z).pi == sum(1 for x in range(2, z + 1) if is_prime(x))
def test_omega(z):
Z = Integer(z)
assert Z.omega == sum(1 for _ in
filter(lambda x: is_prime(x) and not z % x,
range(0, z+1)))
def test_generate_primes(how_many):
primes = generate_primes()
for _ in range(how_many):
assert is_prime(next(primes))