This notebook was prepared by Donne Martin. Source and license info is on GitHub.
For a number to be prime, it must be 2 or greater and cannot be divisible by another number other than itself (and 1).
We'll use the Sieve of Eratosthenes. All non-prime numbers are divisible by a prime number.
Complexity:
Wikipedia's animation:
import math
class PrimeGenerator(object):
def generate_primes(self, max_num):
if max_num is None:
raise TypeError('max_num cannot be None')
array = [True] * max_num
array[0] = False
array[1] = False
prime = 2
while prime <= math.sqrt(max_num):
self._cross_off(array, prime)
prime = self._next_prime(array, prime)
return array
def _cross_off(self, array, prime):
for index in range(prime*prime, len(array), prime):
# Start with prime*prime because if we have a k*prime
# where k < prime, this value would have already been
# previously crossed off
array[index] = False
def _next_prime(self, array, prime):
next = prime + 1
while next < len(array) and not array[next]:
next += 1
return next
%%writefile test_generate_primes.py
import unittest
class TestMath(unittest.TestCase):
def test_generate_primes(self):
prime_generator = PrimeGenerator()
self.assertRaises(TypeError, prime_generator.generate_primes, None)
self.assertRaises(TypeError, prime_generator.generate_primes, 98.6)
self.assertEqual(prime_generator.generate_primes(20), [False, False, True,
True, False, True,
False, True, False,
False, False, True,
False, True, False,
False, False, True,
False, True])
print('Success: generate_primes')
def main():
test = TestMath()
test.test_generate_primes()
if __name__ == '__main__':
main()
Overwriting test_generate_primes.py
%run -i test_generate_primes.py
Success: generate_primes