def solve(count: int = 10001) -> int:
"""Solves problem 7.
Counts prime numbers up to the count and stops
counting once the function has counted primes
equaling the passed in count.
Arguments:
count {int} -- The number of prime numbers to count.
Default is 10001.
Returns:
int -- The last prime number that was counted.
"""
if count <= 0:
return 0
if count == 1:
return 2
if count == 2:
return 3
n_odd = 5
primes_counted = 3
while primes_counted < count:
n_odd += 2
if is_prime(n_odd):
primes_counted += 1
return n_odd
def test_is_prime_with_lte_1(self):
"""Test that False is returned when the number is a number less than or equal to 1."""
not_primes = [-1, 0, 1]
for not_prime in not_primes:
with self.subTest(i=not_prime):
number = not_prime
actual = is_prime(number)
self.assertFalse(actual)
def test_is_prime_with_primes(self):
"""Test that is_prime returns True for the first primes less than 20."""
known_primes = [2, 3, 5, 7, 11, 13, 17, 19]
for prime in known_primes:
with self.subTest(i=prime):
number = prime
actual = is_prime(number)
self.assertTrue(actual)
def test_is_prime_with_not_primes(self):
"""Test that is_prime returns False for non-prime numbers less than 10."""
not_primes = [4, 6, 8, 9]
for not_prime in not_primes:
with self.subTest(i=not_prime):
number = not_prime
actual = is_prime(number)
self.assertFalse(actual)
def solve(limit: int = 2000000) -> int:
"""Solves problem 10.
Computes the sum of all prime numbers less than the limit.
Each number is tested for primality and added to a running
sum if the number is prime.
Arguments:
limit {int} -- Integers less than this number will be tested for primality.
Default is 2000000.
Returns:
int -- The sum of all primes less than the limit.
"""
# TODO: Runs at ~13 sec when limit is 2 mil. Needs optimization.
counter = 0
result = 0
while counter < limit:
if is_prime(counter):
result += counter
counter += 1
return result
def solve(integer: int = 600851475143) -> int:
"""Solves problem 3.
Finds the largest prime of the argument
through trial division by checking
if the factor is a prime. The factors are
checked in reverse order and starts with
the square root of the integer.
Arguments:
integer {int} -- The integer to be factored.
Default is 600851475143
Returns:
int -- The largest prime factor of the integer if found.
"""
prime = None
upper_factor = ceil(sqrt(integer))
for i in range(upper_factor, 0, -1):
if integer % i == 0 and is_prime(i):
prime = i
break
return prime