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Ashutosh Writes
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Ashutosh Writes is a tech-focused blog where practical learning connects with real-world development. It features clear, engaging articles on web development, Python, Java, artificial intelligence, and modern software engineering. From hands-on project tutorials and coding guides to AI concepts and development insights, the blog is designed to simplify complex topics and help developers learn, build, and grow at every stage of their journey.
A prime number, as we know, is a natural number that has exactly two distinct natural number divisors: the number 1 and itself.
We often get questions like the one given below:
Given a number n, print all primes smaller than or equal to n. — e.g. If n is 20, the output should be “2, 3, 5, 7, 11, 13, 17, 19”
Sieve of Eratosthenes is used to get all prime numbers in a given range and is a very efficient algorithm. You can read more about Sieve of Eratosthenes on Wikipedia.
In this algorithm, we follow the following steps to get prime numbers up to n (let’s suppose n = 12):
is_prime = [True, True, True, True, True, True, True, True, True, True, True, True, True]is_prime = [False, False, True, True, True, True, True, True, True, True, True, True, True]is_prime = [False, False, True, True, False, True, False, True, False, True, False, True, False]is_prime = [False, False, True, True, False, True, False, True, False, False, False, True, False]def seive_of_eratosthenes(n):
is_prime = [True for _ in range(n+1)]
is_prime[0], is_prime[1] = False, False
for i in range(2, int(n**0.5)+1):
for j in range(2*i, n+1, i):
is_prime[j] = False
return is_prime
if __name__ == "__main__":
n = int(input("Enter the number upto which : "))
li = seive_of_eratosthenes(n)
for i in range(n+1):
if li[i]:
print(i, end=" ")
This code is a straightforward representation of the steps mentioned above.
We first make a boolean list with all values initialized with True. A value will be False if it is not prime else True. Then we start iterating from 2 to the square root of the number and updating the multiples as False as well. This is done using another ‘for’ loop from 2*i to n+1 with a step of j+1.
In the end, we get our final list and check the values. If the value at any index is True, it means the number is prime and we print the number.
Thank you for reading!