Question

Can anyone give a Thrall explain ERATOSTHENES’ SIEVE

Answer 1

Answer:

See below  

Step-by-step explanation:

The sieve of Eratosthenes is a stepwise method for finding all prime numbers up to a given number n.

Assume that you want to find all the prime numbers between 1 and 100.

Step 1.

Create a square grid with numbers from 1 to 100.

You will be finding numbers in the grid that are composite (not prime) and discarding them. The remaining numbers are the primes.

Step 2.

Mark 1, because it is not a prime.

Step 3.

2 is prime. Mark all multiples of 2, starting from 4 (green in the image below).

Step 4.

3 is prime. Mark all multiples of 3, starting from 9 (blue)

Step 5.

4 is composite, so, mark all multiples of 5, starting from 25 (orange).

Step 6.

6 is composite, so, mark all multiples of 7, starting from 49 (purple).

Step 7.

8, 9, and 10 are composite, and 11² > 100, so we can stop.

All the unmarked numbers are the prime numbers between 1 and 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.