Transcript Prime Numbers Eratosthenes’ Sieve - 2July

Prime Numbers
Eratosthenes’ Sieve
By www.2july.co.uk
Eratosthenes
(ehr-uh-TAHS-thuh-neez)
Eratosthenes was the librarian at
Alexandria, Egypt in 200 B.C.
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.
Eratosthenes’ Sieve
A sieve has holes in it and is used to filter
out liquids from solids.
Eratosthenes’s sieve filters out numbers
to find the prime numbers.
Definition
A Factor – a number that is
multiplied by another to give a
product.
7 x 8 = 56
Factors
Definition
A Factor – a number that
divides exactly into another.
56 ÷ 8 = 7
Factor
Definition
A Prime Number – a number that
has only two factors, itself and 1.
1x7=7
7 is prime because the only numbers
that will divide into it evenly are 1 and 7.
Note: 1 is not a PRIME as it only has 1 factor repeated, 1x1 = 1
Hundreds Chart
On graph paper, make a chart of
the numbers from 1 to 100, with 10
numbers in each row.
A Hundreds Chart
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
1 – Cross out 1; it is not prime.
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
Hint For Next Step
Remember all numbers divisible
by 2 are even numbers.
2 – Leave 2; cross out multiples of 2
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
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.
267
Total of digits = 15
3 divides evenly into 15
267 is a multiple of 3
3– Leave 3; cross out multiples of 3
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
Hint For the Next Step
To find the multiples of 5 look
for numbers that end with the
digit 0 and 5.
385 is a multiple of 5
& 890 is a multiple of 5
because the last digit
ends with 0 or 5.
4– Leave 5; cross out multiples of 5
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
5– Leave 7; cross out multiples of 7
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
6–Leave 11; cross out multiples of 11
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
All the numbers left are prime
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
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