From dd6726771dc8c1762bbd9f547a365d0efab2203c Mon Sep 17 00:00:00 2001
From: 24f3000679shiva <24f3000679@ds.study.iitm.ac.in>
Date: Sun, 25 Jan 2026 23:18:39 +0530
Subject: [PATCH 1/5] Update generate_numbers.py

natural number
---
 generate_numbers.py | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/generate_numbers.py b/generate_numbers.py
index bef48ad..db0f174 100644
--- a/generate_numbers.py
+++ b/generate_numbers.py
@@ -1,6 +1,10 @@
 def natural_numbers(n):
     #Returns the list of natural numbers
     #Code here
+    numbers = []
+    for i in range(1, n + 1):
+        numbers.append(i)
+    return numbers
 
 
 def nth_fibonacci(n):
@@ -9,4 +13,5 @@ def nth_fibonacci(n):
 
 def is_prime(n):
     #Return true if 'n' is prime, otherwise returns false
-    #Code here
\ No newline at end of file
+    #Code here
+    

From 3bf755fd375e78a9ff083c9aaa8dada097ceca6b Mon Sep 17 00:00:00 2001
From: 24f3000679shiva <24f3000679@ds.study.iitm.ac.in>
Date: Sun, 25 Jan 2026 23:19:35 +0530
Subject: [PATCH 2/5] Update generate_numbers.py

fibonacci number
---
 generate_numbers.py | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/generate_numbers.py b/generate_numbers.py
index db0f174..66f2ccd 100644
--- a/generate_numbers.py
+++ b/generate_numbers.py
@@ -10,6 +10,18 @@ def natural_numbers(n):
 def nth_fibonacci(n):
     #Returns n-th fibonacci number
     #Code here
+    if n <= 0:
+        raise ValueError("n must be a positive integer")
+    elif n == 1:
+        return 0
+    elif n == 2:
+        return 1
+    
+    a, b = 0, 1
+    for _ in range(3, n + 1):
+        a, b = b, a + b
+    return b
+
 
 def is_prime(n):
     #Return true if 'n' is prime, otherwise returns false

From 24269a3de794f3f549fab804296af9284c883aac Mon Sep 17 00:00:00 2001
From: 24f3000679shiva <24f3000679@ds.study.iitm.ac.in>
Date: Sun, 25 Jan 2026 23:20:18 +0530
Subject: [PATCH 3/5] Update generate_numbers.py

is_prime
---
 generate_numbers.py | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/generate_numbers.py b/generate_numbers.py
index 66f2ccd..5494806 100644
--- a/generate_numbers.py
+++ b/generate_numbers.py
@@ -26,4 +26,17 @@ def nth_fibonacci(n):
 def is_prime(n):
     #Return true if 'n' is prime, otherwise returns false
     #Code here
+    if n <= 1:
+        return False
+    if n <= 3:
+        return True
+    if n % 2 == 0 or n % 3 == 0:
+        return False
+    
+    i = 5
+    while i * i <= n:
+        if n % i == 0 or n % (i + 2) == 0:
+            return False
+        i += 6
+    return True
     

From 4a289e1b440bbbf2ca437fb3a77cce54e8935008 Mon Sep 17 00:00:00 2001
From: 24f3000679shiva <24f3000679@ds.study.iitm.ac.in>
Date: Sun, 25 Jan 2026 23:22:09 +0530
Subject: [PATCH 4/5] Update generate_numbers.py

is_prime
---
 generate_numbers.py | 17 ++++++-----------
 1 file changed, 6 insertions(+), 11 deletions(-)

diff --git a/generate_numbers.py b/generate_numbers.py
index 5494806..8601972 100644
--- a/generate_numbers.py
+++ b/generate_numbers.py
@@ -26,17 +26,12 @@ def nth_fibonacci(n):
 def is_prime(n):
     #Return true if 'n' is prime, otherwise returns false
     #Code here
-    if n <= 1:
-        return False
-    if n <= 3:
-        return True
-    if n % 2 == 0 or n % 3 == 0:
-        return False
     
-    i = 5
-    while i * i <= n:
-        if n % i == 0 or n % (i + 2) == 0:
+   if n <= 1:
+        return False
+    for i in range(2, int(n**0.5) + 1):
+        if n % i == 0:
             return False
-        i += 6
     return True
-    
+
+

From 0566a3aac549d509b952244d981aaeec138cc6b9 Mon Sep 17 00:00:00 2001
From: 24f3000679shiva <24f3000679@ds.study.iitm.ac.in>
Date: Sun, 25 Jan 2026 23:25:11 +0530
Subject: [PATCH 5/5] Update generate_numbers.py

natural_numbers
---
 generate_numbers.py | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/generate_numbers.py b/generate_numbers.py
index 8601972..d31fc2b 100644
--- a/generate_numbers.py
+++ b/generate_numbers.py
@@ -1,10 +1,7 @@
 def natural_numbers(n):
     #Returns the list of natural numbers
     #Code here
-    numbers = []
-    for i in range(1, n + 1):
-        numbers.append(i)
-    return numbers
+    return list(range(1, n + 1))
 
 
 def nth_fibonacci(n):