Unify O(sqrt(N)) is_prime functions under project_euler (#6258)

* fixes #5434

* fixes broken solution

* removes assert

* removes assert

* Apply suggestions from code review

Co-authored-by: John Law <johnlaw.po@gmail.com>

* Update project_euler/problem_003/sol1.py

Co-authored-by: John Law <johnlaw.po@gmail.com>

project_euler/problem_049/sol1.py

@@ -25,32 +25,46 @@ After that, bruteforce all passed candidates sequences using
 The bruteforce of this solution will be about 1 sec.
 """
 
+import math
 from itertools import permutations
-from math import floor, sqrt
 
 
 def is_prime(number: int) -> bool:
-    """
-    function to check whether the number is prime or not.
-    >>> is_prime(2)
-    True
-    >>> is_prime(6)
+    """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(-800)
-    False
-    >>> is_prime(104729)
+    >>> 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
     """
 
-    if number < 2:
+    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
 
-    for i in range(2, floor(sqrt(number)) + 1):
-        if number % i == 0:
+    # 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