Python/maths/prime_check.py

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"""Prime Check."""
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import math
import unittest
import pytest
def is_prime(number: int) -> bool:
"""Checks to see if a number is a prime in O(sqrt(n)).
A number is prime if it has exactly two factors: 1 and itself.
>>> is_prime(0)
False
>>> is_prime(1)
False
>>> is_prime(2)
True
>>> is_prime(3)
True
>>> is_prime(27)
False
>>> is_prime(87)
False
>>> is_prime(563)
True
>>> is_prime(2999)
True
>>> is_prime(67483)
False
>>> is_prime(16.1)
Traceback (most recent call last):
...
ValueError: is_prime() only accepts positive integers
>>> is_prime(-4)
Traceback (most recent call last):
...
ValueError: is_prime() only accepts positive integers
"""
# precondition
if not isinstance(number, int) or not number >= 0:
raise ValueError("is_prime() only accepts positive integers")
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True
class Test(unittest.TestCase):
def test_primes(self):
assert is_prime(2)
assert is_prime(3)
assert is_prime(5)
assert is_prime(7)
assert is_prime(11)
assert is_prime(13)
assert is_prime(17)
assert is_prime(19)
assert is_prime(23)
assert is_prime(29)
def test_not_primes(self):
with pytest.raises(ValueError):
is_prime(-19)
assert not is_prime(
0
), "Zero doesn't have any positive factors, primes must have exactly two."
assert not is_prime(
1
), "One only has 1 positive factor, primes must have exactly two."
assert not is_prime(2 * 2)
assert not is_prime(2 * 3)
assert not is_prime(3 * 3)
assert not is_prime(3 * 5)
assert not is_prime(3 * 5 * 7)
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if __name__ == "__main__":
unittest.main()