Will it be true if I say "If a number is not divisible by any of the numbers from $2$ to $9$, it is a prime number." If no, can you mention some numbers which defy this statement?
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1Welcome to Mathematics Stack Exchange. Consider $121$, $143$, and $169$ – J. W. Tanner Apr 01 '20 at 05:27
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Thank You J. W. Tanner and JP3112. – Bob Apr 01 '20 at 05:34
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On reading the quoted statement more carefully, I see it says $1$ to $9$. There is no number not divisible by $1$, so the statement is vacuously true – J. W. Tanner Apr 01 '20 at 05:38
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My bad ;P Should be 2-9. I'll fix it – Bob Apr 01 '20 at 05:56
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The statement you quoted is not true.
There are infinitely many composite numbers not divisible by any number from $2$ to $9$.
Examples include $11\times11$, $11\times11\times 11$, $11\times11\times11\times11$, ...,
$13\times13$, $13\times13\times13$, $13\times13\times13\times13$, ..., $17\times17$, ... $19\times19$, ...,
besides $11\times13$, $11\times17$, $11\times19$, ... $13\times17$, ....
J. W. Tanner
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2 is divisible by a number from 1 to 9 but it is prime. The definition that I like to go with for prime numbers is 'a number is prime iff it has exactly 2 divisors'.