Eratosthenes was a Greek mathematician who invented a method for finding prime numbers called Eratosthenes' Sieve. The method involves starting with a list of consecutive integers from 2 to a specified number and systematically removing multiples of primes, leaving the primes. Specifically, beginning with the number 2, all multiples of 2 are crossed out, then all multiples of 3 are crossed out, and so on. The numbers that remain uncovered are the prime numbers within the selected range. This simple and effective method is still used today to identify prime numbers.

1. Prime Numbers Eratosthenes’ Sieve By Monica Yuskaitis

2. Eratosthenes (ehr-uh-MATAHS-thuh-neez) Eratosthenes was the librarian at Alexandria, Egypt in 200 B.C. Note every book was a scroll.

3. Eratosthenes (ehr-uh-TAHS-thuh-neez) Eratosthenes was a Greek mathematician, astronomer, and geographer. He invented a method for finding prime numbers that is still used today. This method is called Eratosthenes’ Sieve.

4. Eratosthenes’ Sieve A sieve has holes in it and is used to filter out the juice. Eratosthenes’s sieve filters out numbers to find the prime numbers.

5. Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

6. Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

7. Definition Prime Number – a number that has only two factors, itself and 1. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

8. Hundreds Chart On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.

9. Hundreds Chart 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

10. 1 – Cross out 1; it is not prime. 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

11. Hint For Next Step Remember all numbers divisible by 2 are even numbers.

12. 2 – Leave 2; cross out multiples of 2 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

13. Hint For Next Step To find multiples of 3, add the digits of a number; see if you can divide this number evenly by 3; then the number is a multiple of 3. 2 6 7 Total of digits = 15 3 divides evenly into 15 267 is a multiple of 3

14. 3– Leave 3; cross out multiples of 3 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

15. To find the multiples of 5 look for numbers that end with the digit 0 and 5. Hint For the Next Step 385 is a multiple of 5 & 890 is a multiple of 5 because the last digit ends with 0 or 5.

16. 4– Leave 5; cross out multiples of 5 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

17. 5– Leave 7; cross out multiples of 7 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

18. 6–Leave 11; cross out multiples of 11 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

19. All the numbers left are prime 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

20. The Prime Numbers from 1 to 100 are as follows: 2,3,5,7,11,13,17,19, 23,31,37,41,43,47, 53,59,61,67,71,73, 79,83,89,97

21. Credits Clipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/ clipgallerylive/default.asp