No
34
- We all know and love
the Positive
Integers:
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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...
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1
is the first positive integer. It is special since it divides all
the positive integers.
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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...
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2
is the first prime number. Now find all the multiples of
2
(even numbers):
- Positive Integers other than 1 which are not
prime numbers are called Composite Numbers.
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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...
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This leaves 3 as the next prime number.
Now find all the multiples of 3:
- We now have identified all the multiples
of 2 and 3. This gives 5 as the next prime:
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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...
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Continue this process by identifying the
multiples of 5 then finding the next prime and then its multiples
and so on:
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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...
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Try this process with the numbers 1 to 100
crossing out the unwanted multiples of each new prime.
- At what stage are there no more
multiples to cross out?
- This sifting out of the composite
numbers was first done by Eratosthenes (275-194BC).
- It is called the "Sieve
of Eratosthenes".
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