Update prime_number.py

Author: py2k5

prime_number.py

@@ -14,3 +14,27 @@ def prime_num(num):
             print(n, 'is a prime number')
 
 prime_num(n)
+
+
+##optimal version
+
+import math
+
+def prime_num(num):
+    if num < 2:
+        return  # No prime numbers less than 2
+
+    print(2, "is a prime number")  # 2 is the only even prime number
+
+    for n in range(3, num + 1, 2):  # Check only odd numbers
+        is_prime = True
+        #If n is not divisible by any number up to its square root, it is prime. This reduces the number of iterations significantly.
+        for x in range(3, int(math.sqrt(n)) + 1, 2):  # Check divisibility up to sqrt(n)
+            if n % x == 0:
+                is_prime = False
+                break
+        if is_prime:
+            print(n, "is a prime number")
+
+# Example usage
+prime_num(20)