The Sieve of Eratosthenes obtains the primes in a given range by eliminating the multiples of primes beginning from 2

[Reset] Day 6 [April 10th, 2026]

Goals:
"Day 3-4: Control structures (if-else, loops)" (Meta AI, personal communication, August 8, 2025)

Notes:
Python for Software Development' textbook by Halvorsen (n.d.):

To solve, the current task: "Create a Python Script where you find all prime numbers between 1 and 200", I learnt that an efficient method that can be used is the Sieve of Eratosthenes (Geeksforgeeks, 2025; Loucka, 2023).
The Sieve of Eratosthenes obtains the primes in a given range by eliminating the multiples of primes beginning from 2 (Geeksforgeeks, 2025; Loucka, 2023). AS you progress, you will discover some multiples are eliminated.

SIEVE OF ERATOSTENES ALGORITHM (Geeksforgeeks, 2025) [With my additional notes]:

def sieve(num): #num is the extent for which we want to check for primes

#we have to monitor if the numbers are prime

prime = [True] * (num + 1)   #we have + 1 because the number in focus has to be captured

p = 2     #2 is the lowest prime number

  
  
  Sieve of Erastostenes algorithm


while p * p <= num: #the product of the prime less than or equal to num. Why? The Sieve of Eratosthenes obtains the primes in a given range by eliminating the multiples of primes beginning from 2.

    if prime[p]: #from the prime list at index p #showing us p = True at that particular prime

    #Mark all multiples of p as non-prime
    for i in range (p * p, num + 1, p):   #this range starts from the square of p and increases as multiples in p steps
        prime[i] = False
p += 1



    

    





  
  
  creating the list of all prime numbers


res = []

for p in range(2, n + 1):

    if prime[p]:

        res.append(p)

return res

Evaluating the code below outputs the prime numbers between 1 and 200:

if name == "main":
n = 200
res = sieve(n)
for ele in res:
print(ele, end=' ')

Output:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199

Summary:
The Sieve of Eratosthenes obtains the primes in a given range by eliminating the multiples of primes beginning from 2.

References: