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I 'm confused about prime number.

It is possible that we can find a not prime number that is greater than 100 and not divided by {2,3,5,7,9}.

because someone said to me that we can check if a number(greater than 100) is prime just to check if it is not divided by {2,3,5,7,9}

Thank you

user3521250
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1 Answers1

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One can check that a number smaller than 100 is a prime just by checking that it is not divisible by 2, 3, 5, 7.

This is because the next prime after 7 is 11, whose square is greater than 100 (hence the test holds if one replaces 100 by 120, note also that checking the divisibility by 9 is useless since 3 divides 9).

Did
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  • thank you Did my question was about the number greater than 100, can we be sure that a number x > 100 is prime just by checking if x is not divisible by all 2,3,5,7. can we have a prime number that is not divisible by 2,3,5,7. – user3521250 Nov 24 '14 at 15:35
  • No // a prime number p is not divisible by any integer n if n is not 1 neither p – user565739 Nov 24 '14 at 15:49
  • @user3521250 Of course not. Example: 121, not divisible by 2,3,5,7, and yet not prime. – Did Nov 24 '14 at 16:47
  • try some of these 121, 143, 187, 209, 253, 319, 143, 169, 221, 247, 299, 377, 187, 221, 289, 323, 391, 493, 209, 247, 323, 361, 437, 551, 253, 299, 391, 437, 529, 667, 319, 377, 493, 551, 667, 841 – george Nov 24 '14 at 16:49
  • @george What do you have against 169? :-) – Did Nov 24 '14 at 16:49