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_046/sol1.py

@@ -19,30 +19,49 @@ prime and twice a square?
 
 from __future__ import annotations
 
-seive = [True] * 100001
-i = 2
-while i * i <= 100000:
-    if seive[i]:
-        for j in range(i * i, 100001, i):
-            seive[j] = False
-    i += 1
+import math
 
 
-def is_prime(n: int) -> bool:
-    """
-    Returns True if n is prime,
-    False otherwise, for 2 <= n <= 100000
+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(23)
+    >>> is_prime(563)
     True
-    >>> is_prime(25363)
+    >>> is_prime(2999)
+    True
+    >>> is_prime(67483)
     False
     """
-    return seive[n]
+
+    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
 
 
-odd_composites = [num for num in range(3, len(seive), 2) if not is_prime(num)]
+odd_composites = [num for num in range(3, 100001, 2) if not is_prime(num)]
 
 
 def compute_nums(n: int) -> list[int]: