Important note: The third, revised edition of the book “prime numbers – things long-known and things new-found” is now available in bookstores. The enclosed CD can now be downloaded in compliance with the terms of use in the download area. The abridged book can be read as PDF or online.

## (Inverse) Riemann spectrum shows resonances at prime numbers

Here is a comprehensive description of the topic in the last two posts about the sum formula. It is already well-known as the “Riemann spectrum of prime numbers”. The authors are Geoffrey Glover, Grant Keane and Rita Post. Link: https://people.uwec.edu/mbirika/M395_Riemann/The_Riemann_Spectrum_of_the_Prime_Numbers.pdf

## Plot of the Inverse Riemann spectrum: resonances of prime numbers

Here is a plot of the Inverse Riemann Spektrum in the range 10 – 100. The first 2000 zeros of Riemann’s Zeta-function have been evaluated. Prime numbers and their powers have been marked on the x-axis (big / small red circles). For Zooming into the picture please click on it.

## Sum formula shows nice resonances at primes and prime powers

The following sum formula which shows very impressive peaks at the positions of primes and their powers. The formula displays the ‘Inverse Riemann spectrum’ of the non trivial roots of the zeta function: Here the sum goes over the imaginary parts of the non trivial zeros of Riemanns Zeta function, taking nmax zeros. The…

## Who finds the christmas tree?

Find the Christmas tree in the following picture! To take part in the game, please click on the link (it may take a few seconds to load the image). You can find out more if you click on the Christmas tree! As a reward you will get a free 1000 digit prime! Find the Christmas…

## 51th Mersenne prime number has been found!

The 51st known Mersenne prime was discovered on December 7, 2018. It is: Source: https://www.mersenne.org.