6.6 LAB: Sieve of Sundaram In this lab, you are going to implement the "Sieve of Sundaram" algorithm which is used to find all odd prime numbers up to a specific integer. The input of the program is an integer n, which will be used to find all the odd prime numbers less than 2n+2. This algorithm is described as follows (Photo credit: Wikipedia https://en.m.wikipedia.org/wiki/File:SieveofSundaram_Animated.gif): 12 3 5e 89 10 i+j+ 2ij 11 12 13 14 15 10 17 18 19 20 List of Primes (2x 39 ) + 1 21 22 23 24 25 26 27 28 29 30 3 5 7 11 13 31 32 33 34 35 36 37 38 39 40 17 19 23 29 31 41 42 43 44 45 40 47 48 49 50 37 41 43 47 53 52 53 5455 50 58 59 59 01 07 51 57 71 73 01 02 03 04 05 ce07 08 e8 09 70 79 71 72 73 74 75 70 77 78 79 80 81 82 83 84 85 80 87 8 89 90 95 90 98 99 100

6.6 LAB: Sieve of Sundaram In this lab, you are going to implement the "Sieve of Sundaram" algorithm which is used to find all odd prime numbers up to a specific integer. The input of the program is an integer n, which will be used to find all the odd prime numbers less than 2n+2. This algorithm is described as follows (Photo credit: Wikipedia https://en.m.wikipedia.org/wiki/File:SieveofSundaram_Animated.gif): 12 3 5e 89 10 i+j+ 2ij 11 12 13 14 15 10 17 18 19 20 List of Primes (2x 39 ) + 1 21 22 23 24 25 26 27 28 29 30 3 5 7 11 13 31 32 33 34 35 36 37 38 39 40 17 19 23 29 31 41 42 43 44 45 40 47 48 49 50 37 41 43 47 53 52 53 5455 50 58 59 59 01 07 51 57 71 73 01 02 03 04 05 ce07 08 e8 09 70 79 71 72 73 74 75 70 77 78 79 80 81 82 83 84 85 80 87 8 89 90 95 90 98 99 100

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

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6.6 LAB: Sieve of Sundaram
In this lab, you are going to implement the "Sieve of Sundaram" algorithm which is used to find all odd prime numbers up to a specific
integer.
The input of the program is an integer n, which will be used to find all the odd prime numbers less than 2n+2.
This algorithm is described as follows (Photo credit: Wikipedia https://en.m.wikipedia.org/wiki/File:SieveofSundaram_Animated.gif):
1
4.
8.
10
i+j+ 2ij
11
12
13
14
15
16
17
18
19
20
List of Primes
(2x 39 ) + 1
21
22
23
24
25
26
27
28
29
30
3
7
11
13
31
32
33
34
35
36
37
38
39
40
17
19
23
29
31
41
42 43
44
45 46 47 48
49
50
37
41
43
47
53
51
52
53
54
55
58
57
58
59
60
59
61
67
71
73
61
62
83
64
65
66
67
88
69
70
79
71
72 73
74
75
76 77
78
79
80
81
82
83
84 85
88
87 88
89
90
91 92
93
94
95
98
97
98
99
100

• start with a list of numbers from 1 to n;
• for every pair of integers i and j where 1<= i<= j and i+j+ 2ij <= n, remove i+j+ 2ij from the list above;
finally, for each remaining number k in the list, 2k+1 is a prime number.
Ex: If the input is 1, the output is:
[3]
Ex: If the input is 2, the output is:
[3, 5]
Ex: If the input is 10, the output is:
[3, 5, 7, 11, 13, 17, 19]
Hint: Use two nested loops to go through the pairs of i and j.

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