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RE: [PrimeNumbers] factorial

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    hello chris i forgot to ask one more thing, from where hav u seen the theoirem please tell Rassel Chris Caldwell wrote: Hello Rassel from
    Message 1 of 4 , Feb 19, 2006
      hello chris

      i forgot to ask one more thing, from where hav u seen the theoirem

      please tell

      Rassel

      Chris Caldwell <caldwell@...> wrote:
      Hello Rassel from Bangladesh.

      > please send also Wilson theorem and its genarelized form.
      > is there is any theorem like p is prime iff p dose not divide
      > (celieng of n/3)! ?

      Yes. To be prime we must have no divisor less than the square root.
      ceiling(n/3) is greater than the square root when n>6. So the theorem
      might be:

      n>6 is prime if it is relatively prime to ceiling(n/3)!

      But of course trial division is faster. You need a higher restriction
      to replace "relatively prime" with divides (consider 25) as you need
      ceiling(n/3) >= 2*sqrt(n).

      There is a similar theorem for ceiling(n/k)! for each k.



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