# Python Math: Print all primes (Sieve of Eratosthenes) smaller than or equal to a specified number

## Python Math: Exercise-21 with Solution

Write a Python program to print all primes (Sieve of Eratosthenes) smaller than or equal to a specified number.

In mathematics, the sieve of Eratosthenes, one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the multiples of 2.

**Pictorial presentation:**

Animation Credits: Author information here

**Sample Solution**:

**Python Code:**

```
def sieve_of_Eratosthenes(num):
limitn = num+1
not_prime_num = set()
prime_nums = []
for i in range(2, limitn):
if i in not_prime_num:
continue
for f in range(i*2, limitn, i):
not_prime_num.add(f)
prime_nums.append(i)
return prime_nums
print(sieve_of_Eratosthenes(100));
```

Sample 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]

**Flowchart:**

**Python Code Editor:**

**Have another way to solve this solution? Contribute your code (and comments) through Disqus.**

**Previous:** Write a Python program to calculate magic square.

**Next:** Write a python program to find the next smallest palindrome of a specified number.

**What is the difficulty level of this exercise?**

Test your Programming skills with w3resource's quiz.

**Weekly Trends and Language Statistics**- Weekly Trends and Language Statistics