Alert icon
We're changing our privacy policy. This stuff matters.  Learn more  Dismiss

How the Zeros of the Zeta Function Predict the Distribution of Primes

Loading...

Sign in or sign up now!
3,449
Loading...
Alert icon
Sign in or sign up now!
Alert icon

Uploaded by on Jul 9, 2009

http://demonstrations.wolfram.com/HowTheZerosOfTheZetaFunctionPredictTheDistr...

The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.

In number theory, Pi(x) is the number of primes less than or equal to x. Primes are very irregular, and so is the graph of Pi(x). This Demonstration shows how to use the zeros (roots) of the Riemann zeta function to get a function that follows the ju...

Contributed by: Robert Baillie

  • likes, 7 dislikes

Link to this comment:

Share to:
see all

All Comments (2)

Sign In or Sign Up now to post a comment!
  • That is just magic! Thanks Riemann to have found this beautiful formula. Unfortunately it is harder to find zeros of zeta than prime.But from the formula is it possible to say how fast it converges? I mean how many zero do you approximately need to have for instance the first 1000primes?

  • Wolfram: please make your videos longer to explain things better!

    When I first learnt how this one (the Riemann-von Mangoldt formula) works, I was simply mesmorised and programmed it (after getting the zeros with an RS formula program) into an Amiga Basic program to see that it really works. Maybe I'll upload a vid of it soon and try to explain...

Loading...

0 / 00Unsaved Playlist Return to active list
    1. Your queue is empty. Add videos to your queue using this button:
      or sign in to load a different list.
    Loading...Loading...Saving...
    • Clear all videos from this list
    • Learn more