On Thu, Mar 7, 2013 at 10:55 AM, viva8698 <

vaseghisam@...> wrote:

> Hi,

>

> I have a question where I need a very very reliable answer:

>

> Does there exist any function in the world to which I can input the first 6 prime numbers and by finding its zeros I could just get the next 12768 prime numbers - and so forth?

Did you google ?

There are explicit formulae for prime(n)

but they are inefficient to compute.

For example, on

http://en.wikipedia.org/wiki/Formula_for_primes
you find

p_n = 1 + \sum_{k=1}^{2(\lfloor n \ln(n)\rfloor+1)} \left(1 -

\left\lfloor{\pi(k) \over n} \right\rfloor\right)

with

\pi(k) := k - 1 + \sum_{j=1}^k \left\lfloor {2 \over j} \left(1 +

\sum_{s=1}^{\left\lfloor\sqrt{j}\right\rfloor} \left(\left\lfloor{ j-1

\over s}\right\rfloor - \left\lfloor{j \over s}\right\rfloor\right)

\right)\right\rfloor

Now these aren't directly given as "roots of polynomials"

even though that could probably be done ;

OTOH I don't understand really well your "and so forth" - can you give

an example for any other sequence of numbers, to see how that should

work ?

Maximilian

>

> I am indeed talkig about a straight forward calculation and not a sieving etc.

>

> I would be deeply thankful for your help.

>

> Thanks in advance

> -Sam

>

>