From 22d6f5ccc0612ea749eb2acc539e44be4051e586 Mon Sep 17 00:00:00 2001
From: sumit Nayak <sumitnayak2006@gmail.com>
Date: Thu, 2 Oct 2025 19:13:15 +0530
Subject: [PATCH 1/2] Faster & Optimized sieve_of_eratosthenes.py

---
 maths/sieve_of_eratosthenes.py | 36 +++++++++++++++-------------------
 1 file changed, 16 insertions(+), 20 deletions(-)

diff --git a/maths/sieve_of_eratosthenes.py b/maths/sieve_of_eratosthenes.py
index 3923dc3e1612..a50d2d9813ee 100644
--- a/maths/sieve_of_eratosthenes.py
+++ b/maths/sieve_of_eratosthenes.py
@@ -1,5 +1,5 @@
 """
-Sieve of Eratosthones
+Sieve of Eratosthenes
 
 The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or
 equal to a given value.
@@ -9,10 +9,10 @@
 
 doctest provider: Bruno Simas Hadlich (https://github.com/brunohadlich)
 Also thanks to Dmitry (https://github.com/LizardWizzard) for finding the problem
+optimized by : Sumit Nayak (https://github.com/Sumit210106/)
 """
 
 from __future__ import annotations
-
 import math
 
 
@@ -38,29 +38,25 @@ def prime_sieve(num: int) -> list[int]:
         msg = f"{num}: Invalid input, please enter a positive integer."
         raise ValueError(msg)
 
-    sieve = [True] * (num + 1)
-    prime = []
-    start = 2
-    end = int(math.sqrt(num))
-
-    while start <= end:
-        # If start is a prime
-        if sieve[start] is True:
-            prime.append(start)
+    if num < 2:
+        return []
 
-            # Set multiples of start be False
-            for i in range(start * start, num + 1, start):
-                if sieve[i] is True:
-                    sieve[i] = False
+    sieve = [True] * (num + 1)
+    prime = [2]
 
-        start += 1
+    # marked all even numbers as non-prime
+    for i in range(3, int(math.sqrt(num)) + 1, 2):
+        if sieve[i]:  
+            for j in range(i * i, num + 1, 2 * i):
+                sieve[j] = False
 
-    for j in range(end + 1, num + 1):
-        if sieve[j] is True:
-            prime.append(j)
+    # collect odd primes
+    for k in range(3, num + 1, 2):
+        if sieve[k]:
+            prime.append(k)
 
     return prime
 
 
 if __name__ == "__main__":
-    print(prime_sieve(int(input("Enter a positive integer: ").strip())))
+    print(prime_sieve(int(input("Enter a positive integer: ").strip())))
\ No newline at end of file

From 77873f384897829b7ee7173fae47f8c7b213cb17 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 2 Oct 2025 13:47:14 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/sieve_of_eratosthenes.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/sieve_of_eratosthenes.py b/maths/sieve_of_eratosthenes.py
index a50d2d9813ee..f935c8d943b2 100644
--- a/maths/sieve_of_eratosthenes.py
+++ b/maths/sieve_of_eratosthenes.py
@@ -46,7 +46,7 @@ def prime_sieve(num: int) -> list[int]:
 
     # marked all even numbers as non-prime
     for i in range(3, int(math.sqrt(num)) + 1, 2):
-        if sieve[i]:  
+        if sieve[i]:
             for j in range(i * i, num + 1, 2 * i):
                 sieve[j] = False
 
@@ -59,4 +59,4 @@ def prime_sieve(num: int) -> list[int]:
 
 
 if __name__ == "__main__":
-    print(prime_sieve(int(input("Enter a positive integer: ").strip())))
\ No newline at end of file
+    print(prime_sieve(int(input("Enter a positive integer: ").strip())))