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Re: New way of counting pi(N)???

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  • richard042@yahoo.com
    Hello, No, not new. Reference LeGendre s prime counting function. Regards, Dick
    Message 1 of 2 , Jan 25, 2005
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      Hello,

      No, not new. Reference LeGendre's prime counting function.

      Regards,

      Dick

      --- In primenumbers@yahoogroups.com, "mcnamara_gio"
      <mcnamara_gio@y...> wrote:
      >
      > Here is a method how to calculate pi(N). (number of primes not
      > exceding N). For a given N calculate these numbers:
      > p-the largest prime so that p<=sqrt(N)
      > q-the largest prime so that q<p
      > a-amount of those numbers which can be divided by 2 and are not more
      > than N
      > b-amount of those numbers which can be divided by 3 but can not be
      > divided by 2 and are not more than N.
      > c-amount of those numbers which can be divided by 5 but can not be
      > divided by 2 and 3 and are not more than N.
      > d-amount of those numbers which can be divided by 7 but can not be
      > divided by 2 and by 3 and by 5 and are not more than N.
      > .......
      > .......
      > .......
      > .......
      > .......
      > .......
      > .......
      > .......
      > m-amount of those numbers which can be divided by p but can not
      > divided by 2, 3, 5, 7,......q and are not more than N.
      > s=a+b+c+d+.....m.
      > Formula for pi(N): pi(N)=N-s-1+pi(sqrt(N)).
      > For example if N=150 then p=11, q=7
      > a=75
      > b=25
      > c=10
      > d=6
      > m=2
      > s=a+b+c+d+.....m=118.
      > pi(sqrt(150))=4
      > So pi(150)=150-118-1+4=35.
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