def find_nth_prime(nth_prime):
"""
Function returns the nth prime of the natural numbers.
:param nth_prime: {int} is nth prime to return in natural numbers
:return: {int} the nth prime in natural numbers
"""
# check input, raise relevant errors
if type(nth_prime) != int:
raise TypeError("Input param 'nth_prime' was not type of int")
if nth_prime <= 0:
raise ValueError("Input param 'nth_prime' was a negative/zero value")
# by the prime number theorem:
# n(lnn) + n((ln(lnn))−1) < pn < n(lnn) + n(ln(lnn)), where n=nth, pn=nth prime for n≥6
if nth_prime >= 6:
upper_bound = math.ceil(nth_prime * math.log(nth_prime) +
nth_prime * math.log(math.log(nth_prime)))
# else the 5th prime caps at 11
else:
upper_bound = 11
# get all primes up to the calculated possible upper bound of the nth prime
primes = eratosthenes_primes(upper_bound)
# return the nth prime from calculated primes
return primes[nth_prime - 1]
def summation_of_primes(limit):
"""
Function will sum all of the primes up to and including the limit given
Uses the sieve of eratosthenes to generate primes
:param limit: {int}
:return: {int} sum of primes up tp limit
"""
# check input, raise relevant errors
if type(limit) != int:
raise TypeError("Input param 'limit' was not type of int")
# initialize sum and get all primes
prime_sum = 0
primes = eratosthenes_primes(limit)
# add up all primes
for prime in primes:
prime_sum = prime_sum + prime
return prime_sum
def test_input_one(self):
self.assertEqual(eratosthenes_primes(1), [])
def test_input_two(self):
self.assertEqual(eratosthenes_primes(2), [2])
def test_input_zero(self):
self.assertEqual(eratosthenes_primes(0), [])
def test_input_negative(self):
self.assertEqual(eratosthenes_primes(-1), [])
def test_large_non_prime(self):
self.assertEqual(eratosthenes_primes(102), [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97, 101
])
def test_small_non_prime(self):
self.assertEqual(eratosthenes_primes(12), [2, 3, 5, 7, 11])
def test_small_prime(self):
self.assertEqual(eratosthenes_primes(7), [2, 3, 5, 7])