Create Sieve_of_Eratosthenes.py

Sieve_of_Eratosthenes.py

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+def sieve_of_eratosthenes(limit):
+    # Step 1: Create a list (sieve) of Boolean values initialized to True.
+    sieve = [True] * (limit + 1)
+
+    # Step 2: Set the first two elements (0 and 1) to False since they are not prime.
+    sieve[0] = sieve[1] = False
+
+    # Step 3: Iterate through the numbers starting from 2 up to the square root of the limit.
+    for i in range(2, int(limit**0.5) + 1):
+        # Step 4: If the current number (i) is marked as prime, mark its multiples as not prime.
+        if sieve[i]:
+            for j in range(i**2, limit + 1, i):
+                # Mark multiples of i as not prime by setting their values to False.
+                sieve[j] = False
+
+    # Step 5: Collect the prime numbers (marked as True) into a list.
+    primes = [i for i in range(2, limit + 1) if sieve[i]
+
+    # Step 6: Return the list of prime numbers.
+    return primes