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.