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.
<em>Mark 1</em>, because it is not a prime.
Step 3.
2 is prime. Mark all <em>multiples of 2</em>, starting from 4 (green in the image below).
Step 4.
3 is prime. Mark all <em>multiples of 3</em>, starting from 9 (blue)
Step 5.
4 is composite, so, <em>mark all multiples of 5</em>, starting from 25 (orange).
Step 6.
6 is composite, so, <em>mark all multiples of 7</em>, starting from 49 (purple).
Step 7.
8, 9, and 10 are composite, and 11² > 100, so we can <em>stop</em>.
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.
