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

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• 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

<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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