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Eratosthenes |
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Eratosthenes of Cyrene 276 - 200 BC |
A modified version of the method in this example is still used in number theory research.
| Step 1: Write down all the integers between 2 and 20. | ||||||||||||||||||
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2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
| Step 2: Label all the multiples of 2. | ||||||||||||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
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* |
* |
* |
* |
* |
* |
* |
* |
* |
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| Step 3: Take the next number, 3 in this example and label all its multiples. | ||||||||||||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
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* |
* |
* |
* |
* |
* |
* |
* |
* |
* |
* |
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| Repeat step 3, until there are no new unlabelled numbers. Unlabelled numbers are the prime numbers: | ||||||||||||||||||
| 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |||||||||||