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dcc387631d
* improved prime_check
* updating DIRECTORY.md
* included suggested changes
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
86 lines
2.2 KiB
Python
86 lines
2.2 KiB
Python
"""Prime Check."""
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import math
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import unittest
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def is_prime(number: int) -> bool:
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"""Checks to see if a number is a prime in O(sqrt(n)).
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A number is prime if it has exactly two factors: 1 and itself.
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>>> is_prime(0)
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False
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>>> is_prime(1)
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False
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>>> is_prime(2)
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True
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>>> is_prime(3)
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True
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>>> is_prime(27)
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False
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>>> is_prime(87)
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False
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>>> is_prime(563)
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True
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>>> is_prime(2999)
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True
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>>> is_prime(67483)
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False
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"""
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# precondition
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assert isinstance(number, int) and (
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number >= 0
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), "'number' must been an int and positive"
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if 1 < number < 4:
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# 2 and 3 are primes
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return True
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elif number < 2 or number % 2 == 0 or number % 3 == 0:
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# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
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return False
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# All primes number are in format of 6k +/- 1
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for i in range(5, int(math.sqrt(number) + 1), 6):
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if number % i == 0 or number % (i + 2) == 0:
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return False
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return True
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class Test(unittest.TestCase):
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def test_primes(self):
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self.assertTrue(is_prime(2))
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self.assertTrue(is_prime(3))
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self.assertTrue(is_prime(5))
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self.assertTrue(is_prime(7))
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self.assertTrue(is_prime(11))
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self.assertTrue(is_prime(13))
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self.assertTrue(is_prime(17))
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self.assertTrue(is_prime(19))
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self.assertTrue(is_prime(23))
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self.assertTrue(is_prime(29))
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def test_not_primes(self):
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self.assertFalse(
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is_prime(-19),
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"Negative numbers are excluded by definition of prime numbers.",
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)
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self.assertFalse(
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is_prime(0),
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"Zero doesn't have any positive factors, primes must have exactly two.",
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)
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self.assertFalse(
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is_prime(1),
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"One only has 1 positive factor, primes must have exactly two.",
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)
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self.assertFalse(is_prime(2 * 2))
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self.assertFalse(is_prime(2 * 3))
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self.assertFalse(is_prime(3 * 3))
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self.assertFalse(is_prime(3 * 5))
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self.assertFalse(is_prime(3 * 5 * 7))
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if __name__ == "__main__":
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unittest.main()
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