def get_prime_factors(num: int, prime_list: list = None) -> list:
"""Returns a list of tuples containing prime factors and their multiplicty
To speed up repeated calculations, can optionally pass in a list of primes
which will be used to generate the list of prime factors.
>>> get_prime_factors(12)
[(2, 2), (3, 1)]
>>> get_prime_factors(14)
[(2, 1), (7, 1)]
>>> get_prime_factors(2)
[(2, 1)]
>>> get_prime_factors(4)
[(2, 2)]
"""
upper_bound = math.ceil(num / 2) + 1
if not prime_list:
prime_list = [prime for prime in primes.Primes(upper_bound)]
prime_factors = []
for prime in prime_list:
temp = num
multiplicity = 0
temp, remainder = divmod(temp, prime)
while remainder == 0 and temp >= 1:
multiplicity += 1
temp, remainder = divmod(temp, prime)
if multiplicity > 0:
prime_factors.append((prime, multiplicity))
if prime > upper_bound:
break
if not prime_factors:
prime_factors = [(num, 1)]
return prime_factors
def test_in_primes():
primes_under_ten = primes.Primes(10)
assert 3 in primes_under_ten
assert 4 not in primes_under_ten
def test_len_primes():
primes_under_ten = primes.Primes(10)
assert len(primes_under_ten) == 4
def test_largest_prime():
primes_under_thousand = primes.Primes(10**3)
largest_prime_under_thousand = primes_under_thousand.largest_prime()
assert largest_prime_under_thousand == 997
def test_reversed_primes():
primes_under_ten = primes.Primes(10)
primes_under_ten_reversed = [prime for prime in reversed(primes_under_ten)]
assert primes_under_ten_reversed == [7, 5, 3, 2]
def test_iter_primes():
primes_under_ten = primes.Primes(10)
primes_under_ten_list = [prime for prime in primes_under_ten]
assert primes_under_ten_list == [2, 3, 5, 7]