Mathematics 1 ESO – Unit 3 FACTORS AND MULTIPLES page 30 activity 11

The “Sieve of Eratosthenes”

The Sieve of Eratosthenes is a technique to find all the prime numbers below a certain value. For example, below 40

We put all the numbers below 40 (except number 1) on a table:

2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39

 

1st: we take number 2 and we delete all the multiples of 2.

2 3 5 7
9 11 13 15
17 19 21 23
25 27 29 31
33 35 37 39

 

2nd: we take the next number not deleted, number 3 and we delete all the multiples of 3.

2 3 5 7
11 13
17 19 23
25 29 31
35 37

 

3rd: we take the next number not deleted, number 5 and we delete all the multiples of 5.

2 3 5 7
11 13
17 19 23
29 31
37

We continue until all the numbers in the table are taken or deleted The taken numbers are the prime numbers.

Activity 11

Do the Sieve of Eratosthenes for all the prime numbers below 100