# Python: Sieve of Eratosthenes method, for computing prime number

## Python List: Exercise - 34 with Solution

Write a Python program that uses the Sieve of Eratosthenes method to compute prime numbers up to a specified number.

Note: In mathematics, the sieve of Eratosthenes (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous), one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit.

From Wikipedia Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime's square).

**Sample Solution:**

**Python Code:**

```
# Define a function named 'prime_eratosthenes' that generates prime numbers using the Sieve of Eratosthenes algorithm
def prime_eratosthenes(n):
prime_list = [] # Create an empty list to store prime numbers
# Iterate through the numbers from 2 to 'n'
for i in range(2, n+1):
if i not in prime_list:
# If 'i' is not in the 'prime_list,' it's a prime number; print it
print(i)
# Mark all multiples of 'i' as non-prime by adding them to 'prime_list'
for j in range(i*i, n+1, i):
prime_list.append(j)
# Call the 'prime_eratosthenes' function with 'n' set to 100 to generate prime numbers
# The function does not have a return value, so it prints the prime numbers directly
prime_eratosthenes(100)
```

Sample Output:

2 3 5 7 11 ------- 79 83 89 97 None

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