changes implementation of primality testing to be uniform

data_structures/hashing/number_theory/prime_numbers.py

@@ -3,18 +3,48 @@
  module to operations with prime numbers
 """
 
+import math
+
 
 def is_prime(number):
+ """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
  """
- it's not the best solution
- """
- special_non_primes = [0, 1, 2]
- if number in special_non_primes[:2]:
- return 2
- elif number == special_non_primes[-1]:
- return 3
 
- return all(number % i for i in range(2, number))
+ # precondition
+ assert isinstance(number, int) and (
+ number >= 0
+ ), "'number' must been an int and positive"
+
+ if 1 < number < 4:
+ # 2 and 3 are primes
+ return True
+ elif number < 2 or not number % 2:
+ # Negatives, 0, 1 and all even numbers are not primes
+ return False
+
+ odd_numbers = range(3, int(math.sqrt(number) + 1), 2)
+ return not any(not number % i for i in odd_numbers)
 
 
 def next_prime(value, factor=1, **kwargs):

maths/prime_check.py

@@ -29,6 +29,11 @@ def is_prime(number: int) -> bool:
  False
  """
 
+ # precondition
+ assert isinstance(number, int) and (
+ number >= 0
+ ), "'number' must been an int and positive"
+
  if 1 < number < 4:
  # 2 and 3 are primes
  return True