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Transcript 
Prime Numbers
Lecture L4.4
Sieve of Eratosthenes
Find prime numbers using
Sieve of Eratosthenes
// first create an array of flags, where
// each member of the array stands for a odd number
// starting with 3.
for (j = 0; j < size; j++)
{
flags[j] = 1;
}
size = 1024
j
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Find prime numbers using
Sieve of Eratosthenes
primeCount = 0;
for (j = 0; j < size; j++)
{
if (flags[j] == 1)
{
// found a prime, count it
primeCount++;
// now set all of the multiples of
// the current prime number to false
// because they couldn't possibly be
a = 2*j + 3; // odd numbers starting
b = a + j;
while(b < size)
{
flags[b] = 0;
b = b + a;
}
}
}
j
0
1
2
3
4
5
6
7
8
prime
with 3 9
10
11
12
13
14
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
a
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
b
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
Find prime numbers using
Sieve of Eratosthenes
primeCount = 0;
for (j = 0; j < size; j++)
{
if (flags[j] == 1)
{
// found a prime, count it
primeCount++;
// now set all of the multiples of
// the current prime number to false
// because they couldn't possibly be
a = 2*j + 3; // odd numbers starting
b = a + j;
while(b < size)
{
flags[b] = 0;
b = b + a;
}
}
}
j
0
1
2
3
4
5
6
7
8
prime
with 3 9
10
11
12
13
14
15
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
a
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
b
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
Find prime numbers using
Sieve of Eratosthenes
primeCount = 0;
for (j = 0; j < size; j++)
{
if (flags[j] == 1)
{
// found a prime, count it
primeCount++;
// now set all of the multiples of
// the current prime number to false
// because they couldn't possibly be
a = 2*j + 3; // odd numbers starting
b = a + j;
while(b < size)
{
flags[b] = 0;
b = b + a;
}
}
}
j
0
1
2
3
4
5
6
7
8
prime
with 3 9
10
11
12
13
14
15
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
a
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
b
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
Find prime numbers using
Sieve of Eratosthenes
primeCount = 0;
for (j = 0; j < size; j++)
{
if (flags[j] == 1)
{
// found a prime, count it
primeCount++;
// now set all of the multiples of
// the current prime number to false
// because they couldn't possibly be
a = 2*j + 3; // odd numbers starting
b = a + j;
while(b < size)
{
flags[b] = 0;
b = b + a;
}
}
}
j
0
1
2
3
4
5
6
7
8
prime
with 3 9
10
11
12
13
14
15
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
a
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
b
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
Find prime numbers using
Sieve of Eratosthenes
primeCount = 0;
for (j = 0; j < size; j++)
{
if (flags[j] == 1)
{
// found a prime, count it
primeCount++;
// now set all of the multiples of
// the current prime number to false
// because they couldn't possibly be
a = 2*j + 3; // odd numbers starting
b = a + j;
while(b < size)
{
flags[b] = 0;
b = b + a;
}
}
}
j
0
1
2
3
4
5
6
7
8
prime
with 3 9
10
11
12
13
14
15
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
a
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
b
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
Find prime numbers using
Sieve of Eratosthenes
primeCount = 0;
for (j = 0; j < size; j++)
{
if (flags[j] == 1)
{
// found a prime, count it
primeCount++;
// now set all of the multiples of
// the current prime number to false
// because they couldn't possibly be
a = 2*j + 3; // odd numbers starting
b = a + j;
while(b < size)
{
flags[b] = 0;
b = b + a;
}
}
}
j
0
1
2
3
4
5
6
7
8
prime
with 3 9
10
11
12
13
14
15
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
a
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
b
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
Find prime numbers using
Sieve of Eratosthenes
primeCount = 0;
for (j = 0; j < size; j++)
{
if (flags[j] == 1)
{
// found a prime, count it
primeCount++;
// now set all of the multiples of
// the current prime number to false
// because they couldn't possibly be
a = 2*j + 3; // odd numbers starting
b = a + j;
while(b < size)
{
flags[b] = 0;
b = b + a;
}
}
}
j
0
1
2
3
4
5
6
7
8
prime
with 3 9
10
11
12
13
14
15
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
a
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
b
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
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