Rule to check a given
natural number to be prime
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Step
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Procedure
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Example
1
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Example
2
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1.
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Let n be the given natural number.
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Let n = 73
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Let n = 133
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2.
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Identify greatest perfect square
natural number m2 just less than n
i.e. m2 < n.
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Since immediate smaller perfect square
is 64 therefore m = 8
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Since immediate smaller perfect square
is 121 therefore m = 11
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3.
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Identify all prime numbers less than
or equal to m.
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Prime numbers < 8 are 2,3,5,7.
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Prime numbers ≤ 11 are 2,3,5,7,11
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4.
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The given number n would be a prime
number if it is not divisible by any of the above prime numbers.
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Since 73 is not divisible by any of
these therefore 73 is prime,
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Since 133 is divisible by 7 therefore 133 is not a prime number.
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