http://demonstrations.wolfram.com/HowTheZerosOfTheZetaFunctionPredictTheDistr...
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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
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?
nicodougy 10 months ago
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...
ortega24024 2 years ago