Unify primality checking (#6228)

* renames prime functions and occurances in comments

* changes implementation of primality testing to be uniform

* adds static typing as per conventions

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

data_structures/hashing/double_hash.py

@@ -1,6 +1,6 @@
 #!/usr/bin/env python3
 from .hash_table import HashTable
-from .number_theory.prime_numbers import check_prime, next_prime
+from .number_theory.prime_numbers import is_prime, next_prime
 
 
 class DoubleHash(HashTable):
@@ -15,7 +15,7 @@ class DoubleHash(HashTable):
 
         next_prime_gt = (
             next_prime(value % self.size_table)
-            if not check_prime(value % self.size_table)
+            if not is_prime(value % self.size_table)
             else value % self.size_table
         )  # gt = bigger than
         return next_prime_gt - (data % next_prime_gt)

data_structures/hashing/number_theory/prime_numbers.py

@@ -3,25 +3,55 @@
     module to operations with prime numbers
 """
 
+import math
 
-def check_prime(number):
-    """
-    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))
+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
+    """
+
+    # 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):
     value = factor * value
     first_value_val = value
 
-    while not check_prime(value):
+    while not is_prime(value):
         value += 1 if not ("desc" in kwargs.keys() and kwargs["desc"] is True) else -1
 
     if value == first_value_val: