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Samuel Marateck
© 2010
• The Sieve of Eratosthenes
Place a 0 in all slots
• X = 26*[0]
Place 0’s in all slots.
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10
11
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21
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24
25
Start with 2
for j in range(2, √25):
Start with 2
for j in range(2, √25):
if x[j] == 0:
Start with 2
for j in range(2, √25):
if x[j] == 0:
index = 2*j
Start with the 2 slot.
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10
11
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25
for j in range(2, √25):
if x[j] == 0:
index = 2*j
while index < 25:
x[index] = 1
Place a 1 in the 4 slot.
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10
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25
for j in range(2, √25):
if x[j] == 0:
index = 2*j
while index < 25:
x[index] = 1
index = index + j
Then in the 6 slot.
0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10
11
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24
25
Continue.
0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10
11
12
13
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15
16
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18
19
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21
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24
25
Continue.
0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10
11
12
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15
16
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21
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24
25
Continue.
0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10
11
12
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21
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24
25
Place 1’s in all multiples of 2 slots.
0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
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24
25
Since there is a 0 in the 3 slot,3 is prime
0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
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25
There is a 1 already in the 6 slot.
0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
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25
Place a 1 in the 9 slot.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
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21
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25
The 12 slot already has a 1.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
13
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15
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25
Then a 1 in the 15 slot.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
13
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15
16
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21
22
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24
25
Then a 1 in the 21 slot.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
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15
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24
25
Now there is a 1 in all multiple of 3 slots.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
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15
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21
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24
25
Skip the 4 slot since it has a 1.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
12
13
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15
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21
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23
24
25
There is a 0 in the 5 slot,so 5 is prime.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
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25
Place a 1 in multiple of 5 slots.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0
1 2 3 4 5 6 7 8 9 10
11
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25
The only non-zero slot is 25.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1
1 2 3 4 5 6 7 8 9 10
11
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25
Since √25 is 5 we stop here.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1
1 2 3 4 5 6 7 8 9 10
11
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25
Starting with 2, all the slots with 0’s are prime numbers.
0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1
2 3 5 7 11
13
17
19
23
